NEW ORLEANS — According to script? Keeping with the narrative?

Not your 2016 Raiders.

The Raiders and Michael Crabtree turned the story line upside down in their season opener. They bucked both their history and coaching convention, beating the Saints in the Superdome in a 35-34 thriller.

And it was a Crabtree grab of a fade route in the end zone that clinched the victory. Which just goes to show you how narratives can change.

Crabtree couldn’t sleep Saturday night. His head was filled with thoughts about playing in the Superdome.

“I have memories,” Crabtree said.

They’re the same memories that have haunted the 49ers for more than three years. Memories of being the targeted option for Colin Kaepernick in Super Bowl XLVII. On second down. On third down. On fourth down. Each pass could have won the game for the 49ers. All fell incomplete. The images kept Crabtree awake in his hotel room.

“All of that,” he said. “The last play, it ended bad.

“This time, the last play ended good.”

Really good.

And this could be the start of something special. There are high expectations for the Raiders this season. Many have penciled them in as a playoff team. But at times Sunday, they looked like the same old Raiders. So it was refreshing to see how the story line changed.

The Raiders shook off a four-year streak of losing their opening game. They rallied against their history of falling short to storm back from a 14-point deficit in the third quarter. They overcame their mistakes: 14 penalties for 141 yards. They didn’t wilt in the face of Drew Brees’ 423 passing yards and four touchdowns.

And when it came time to decide the game, their head coach didn’t do the safe, conservative thing. Jack Del Rio didn’t adhere to the book, didn’t opt to kick an extra point to tie the game. Instead, he told his players, “When we go score here, we are going to go for two.” And then they did just that.

“That kind of belief gives us so much confidence,” quarterback Derek Carr said. “It makes you want to fight for him. So when he says we’re going to go down the field and score and then go for two, you say, ‘Yes, sir.’”

That type of confidence will continue to grow after a win like Sunday’s.

“This year, we’re talking about learning how to win, learning how to close these games,” Del Rio said.

And they’re talking a little smack in the process. After the game, ESPN tweeted that “Based on ESPN’s win prob. model, Raiders had 51% chance to win if they kicked PAT & 44% chance if they went for 2.” After the game Del Rio retweeted that with the comment: “Good thing ESPN isn’t coaching the Raiders.”

Yes, everyone on the Raiders was feeling good. It’s hard to overstate the importance of Sunday’s victory. Sure, the Saints are a flawed team, but they are also difficult to beat in their home, especially when they have a lead. The place is deafeningly loud and can rattle young quarterbacks to their core.

Carr doesn’t rattle easily. He said he was frustrated by some of the coverages the Saints showed him, and credited his former head coach and current New Orleans defensive coordinator Dennis Allen for that.

“He knows me. We knew he would do things that would disrupt me,” Carr said.

Still, Carr kept leading his team back. With less than a minute left, Carr found Seth Roberts for a 10-yard touchdown. Roberts had dropped an earlier pass, but he pulled in this one.

And then Carr lofted the ball into the end zone for Crabtree.

“I just knew Crab was going to make that play,” said Amari Cooper. “He’s made it a lot of times.”

Well, he’s also not made it on one memorable occasion. This time, the pass came in the opposite end zone from where the 49ers’ futile Super Bowl drive ended. This time, Crabtree pulled it in. This time, he was on the winning side.

Nobody seemed surprised by Del Rio’s risky call. Even Brees admiringly called it “ballsy.”

“He’s got a lot of trust in us, and we have trust in him,” Crabtree said of his coach.

Even with the lead, the Raiders were playing with fire. Crabtree drew an unsportsmanlike-conduct penalty for celebrating. Brees got the ball back with 40 seconds on the clock. But the Raiders’ defense held, and the Saints had to settle for a 61-yard field- goal try that went wide left.

Then, finally, the Raiders could exhale. They can say they are 1-0 for the first time since Hue Jackson coached the Jason Campbell-led Raiders to a win in Denver in 2011.

“You’ve gotta have heart,” Crabtree said. “We showed that today.”

And they rewrote the script in the process.

Ann Killion is a San Francisco Chronicle columnist. Email: akillion@sfchronicle.com Twitter: @annkillion