Photo: Scott Strazzante / The Chronicle Photo: Ezra Shaw, Getty Images Photo: Michael Appleton/NY Daily News Archive Via Getty Images Photo: Darryl Bush / SFC Photo: Michael Maloney / SFC Photo: Darryl Bush / SFC Photo: Santiago Mejia, The Chronicle Photo: Santiago Mejia / The Chronicle

MIAMI — Joe Staley’s 13-season career is a testament to sustained excellence, but it also has been bookended by two games in which accomplished pass rushers treated the 49ers’ left tackle like a turnstile.

Staley’s response to those starts, perhaps his worst in the NFL, highlight qualities that have made him one of the best blindside protectors of his generation.

In a recent interview, Staley, 35, reflected on those moments from his rookie season and recent past. And he did so before a game that could provide the pinnacle of a career filled with adversity and achievement, one that has included six Pro Bowls, seven 10-loss seasons, four NFC Championship Games and two broken legs.

Staley, the team’s longest-tenured player, understands Sunday’s date with the Chiefs in Super Bowl LIV could be his last chance to win a title.

“My whole thing has always been going to a Super Bowl and winning a Super Bowl,” Staley said. “I just want to win one so badly. It would be a huge void if it didn’t happen.”

Why is Staley, the No. 28 pick in 2007, one of five selections from his first-round class, still playing? How is he still playing at such a high level?

It’s a reflection of his self-belief, work ethic and competitive fury, intangibles born or summoned from his worst moments.

First, there was his sixth career start in 2007. In a 33-15 road loss to the Giants, Staley was dominated by Hall of Fame defensive end Michael Strahan. After Strahan had 2½ sacks and three quarterback hits, Staley was so humiliated that he avoided teammates in the locker room, boarded the empty team bus and called his dad, Butch, in a shaky panic.

“I told him, ‘This s— is hard, man,’” Staley said. “‘I don’t feel like I belong here. These guys are on a different level.’ … I was feeling embarrassed. Feeling overwhelmed. Feeling, ‘What did I get myself into?’”

Said Butch Staley: “My heart was really hurting for him. Because I knew he’d be really hard on himself.”

Indeed, this was not the wisecracking tackle who has hosted the off-the-wall “Joe Show” and is known for enthusiastic and awful karaoke. Staley was so high-strung and buttoned-up as a rookie that he was nicknamed “G.I. Joe.” Three years earlier, the man who started his college career at tight end was a 250-pound sophomore tackle at Central Michigan, the lone Division I school to offer him a scholarship.

He felt overwhelming pressure to prove himself after the 49ers had traded up with the Patriots to select him in the first round. His rookie season already had started poorly before he was humiliated by Strahan.

He was so anxiety-ridden before the game that he didn’t sleep. He chugged three Red Bulls prior to kickoff in a futile attempt to get energy before facing a player who inspired awe.

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“I’d had no aspirations of playing beyond Central Michigan,” Staley said. “I just thought it was just the coolest thing I was playing college football. I just did not see my career going to where it went — being a first-round pick. Ever.

“So I was surprised. I was like, ‘I guess I’m good.’ But I never saw myself as being amazing. So I put a lot of pressure on myself: ‘They’re expecting me to perform.’ And I guess that’s why I felt a little emotional — helpless, almost, in that moment.”

The moment didn’t break him. Instead, assisted by his dad’s counsel, the 23-year-old who was resembling a first-round bust realized he hadn’t given himself a chance.

It was a wake-up call to do everything possible to make himself better so he could face the NFL’s best. It was about having self-belief and trusting in exhaustive preparation, rather mundane athletic truths that have made Staley the player he is.

“I realized it was all stuff I built up in my own head about what this person can do instead of what I can do,” Staley said. “It was a pretty huge moment for my career as far as: I needed to work as hard as I can to control what I can control. Not worry about the player I’m going against and what his accolades are. I kind of flipped that mentally.

“It wasn’t like the next day I was fixed. But I just started to develop those habits. … It was so huge for my career. And that’s why I always return to that story as far as being a big turning point for me.”

The second story? It’s not about Staley not believing in himself. Rather, it’s about others no longer believing in him.

In November, in his first game back after missing five games because of a broken fibula, Staley was overwhelmed by Pro Bowl pass rusher Jadeveon Clowney in a 27-24 overtime loss to Seattle that was the 49ers’ first loss of the season.

Staley had returned too quickly from his injury and complications from his rehab included back issues that plagued him against Clowney, who would be named the NFC Defensive Player of the Week based on his performance. In addition, Staley suffered a broken and dislocated finger during the game that required surgery and sidelined him for three weeks.

His health issues made him resemble a broken-down 35-year-old. And he read on social media and elsewhere that he was washed up and the 49ers were better off sticking with Daniel Brunskill, his impressive replacement when he’d been sidelined.

Asked about being written off, Staley paused a few seconds before responding.

“This is going to sound bad, what I’m about to say,” Staley began. “We were at the time 8-0 when I came back. The team was playing really well and we had a lot of fans that weren’t around that all the sudden wanted to be fans. I think people forgot what I’ve done for this franchise and what kind of player I am.

“That motivated me a lot, though. I felt almost disrespected. … It was pinned on me as being the reason (we lost) because I’m washed up. I’m not.”

Staley insists the criticism wasn’t hurtful, just angering. His wife of six years, Carrie, a former professional soccer player, could see her husband was affected by the criticism.

“He would try not to let it show, but I knew it was upsetting to him,” Carrie said. “And I also know he was nowhere near 100%. It was really tough to see him feeling so poorly. And to feel like people were turning on him was rough. It definitely motivated him to get healthy and to get back to where he is now.”

Yes, Staley has taken out his displeasure on opponents.

In two playoff wins, Staley, in peak form, has helped pave the path for an offense that has averaged 32 points, 235.5 rushing yards and 5.3 yards a carry in 17-point wins over the Vikings and Packers, respectively.

Much has changed since Staley made his only other Super Bowl appearance, a loss to the Ravens in February 2013.

Professionally, he’s likely in the twilight of his career, although he’s signed through 2021 and has said Sunday’s game won’t be his last, regardless of the outcome.

Personally, he’s now married with two daughters: Grace, 5, and Audrey, 2. Carrie says her husband is a “goofy” and high-energy dad. He often makes his entrance home from work by screaming his arrival, which prompts his daughters to come running after him before they head to the backyard jungle gym.

“This is really sweet this is happening now,” Butch Staley said. “Because Joe has his wife and daughters that he’s focused on. His world has gotten bigger and richer. It’s special for us.”

Staley will have a void if his career ends without a title, but he’s far better equipped to handle life’s disappointments than he was 13 years ago.

He has gained so much throughout his NFL life: a family, professional success, knowledge that he didn’t waste his gift and perspective.

In a question inspired by two of the worst games of his career, he was asked how he would have reacted if Strahan had dominated him in today’s social-media age.

“Oh, I would have really cracked,” Staley said, laughing. “It would be like, “Hey, dad, they’re talking bad about me on the internets!’”

Eric Branch covers the 49ers for The San Francisco Chronicle. Email: ebranch@sfchronicle.com Twitter: @Eric_Branch