NEW ORLEANS -- Mark Ingram was happy because he was scoring touchdowns again.

Jairus Byrd was happy because he was intercepting passes again.

And the New Orleans Saints were happy because they gave a terrific, complete performance that was a night-and-day difference from the last time they played the Tampa Bay Buccaneers.

Unfortunately, Saturday's 31-24 victory won't be enough to get New Orleans (7-8) into the playoffs. But it was a nice redemption win all around, just 13 days after the Saints destroyed their fading playoff hopes with their biggest flop of the year -- a 16-11 loss in Tampa.

"I know that we've had some tough moments this year that have prevented us from being in a playoff position, but I also believe that you go through a lot of those things for a reason, and that you learn along the way, and it's what enables you to have success in the future," said Saints quarterback Drew Brees, who threw for 299 yards and a touchdown, redeeming his ugly performance at Tampa Bay two weeks ago (three interceptions and zero TDs). "I feel like we're right there, knocking on the door, and we've got a lot of the right pieces in place."

Saturday's performance also won't guarantee that coach Sean Payton will stay in New Orleans beyond this season. But it was a reminder of what I wrote about the annual Payton coaching rumors on Saturday morning: that the Saints aren't eager to let him go because they genuinely feel like this team is pointing in the right direction and has shown more potential than the previous two 7-9 campaigns.

Jairus Byrd celebrates after one of his two interceptions on Saturday against Tampa Bay. Chuck Cook/USA TODAY Sports

Ingram had a monster day on Saturday, with 90 yards on 18 carries, including touchdown runs of 14 and 6 yards. He also had a two-point conversion run and a game-clinching 10-yard run on third-and-1 with less than two minutes remaining, allowing the Saints to take a knee to run out the clock.

Ingram's performance was perhaps the most noteworthy on Saturday, because it came just six days after his sideline tirade and shouting at Payton when the running back was upset that he didn't get two goal-line opportunities in the fourth quarter.

Ingram explained at the time that he is always competitive but needs to control his emotions better. That's exactly what he appeared to be doing with several hard runs and broken tackles on Saturday. Ingram insisted the two weren't related, though.

"It was done after the game, [it's] a new week, a new game. And I just tried to keep my same mentality like I always do -- to run physical and bring a spark to my team," said Ingram, who credited the offensive line first and the receivers, tight ends and fullback John Kuhn -- who was jokingly prodding Ingram from the next locker. "They blocked their butt of for me today."

Ingram now has a career-high 1,230 yards from scrimmage this season. He needs 60 rushing yards next Sunday against the Atlanta Falcons to achieve his first 1,000-yard rushing season. He has nine total touchdowns on the year, matching his career high.

"Man, I thought he ran well," Payton said of Ingram. "I thought it was noticeably different in the first half with a few of our handoffs and how we blocked them. I think we averaged 10 yards a carry on just a power play, which is always a tough play in our league. But those guys up front did a really good job. I'm proud of 'em."

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Byrd, meanwhile, had his first two interceptions of the season on Saturday -- one in each half -- as well as a 4-yard tackle for loss in what was easily his best performance in three years with the Saints.

Byrd's time in New Orleans has largely been a huge disappointment because of a major knee injury he suffered in 2014 and some inconsistent play when he has been healthy. But Payton said Thursday that Byrd had been playing his best football in New Orleans over the past six weeks. Byrd agreed, saying the only thing missing was the turnovers.

"It's been a long time coming. But like I said this week, things are feeling good for me. You know, it took longer than I wanted, obviously, but I feel good," Byrd said. "I mean, I've never questioned what I can do or my talent. That's not a fluke; you don't do anything in this league as a fluke. Obviously injuries happen, no one wants those things, and it just took me a little bit longer than I would've liked and that a lot of people would've liked. ... So I'm just thanking God for my health."

Payton reiterated how well Byrd has been playing lately and called his two interceptions Saturday "really the difference in the game."

Byrd, 30, was a turnover machine during his first five years with the Buffalo Bills -- posting 22 interceptions and 11 forced fumbles -- which is why he was named to three Pro Bowls. But he had just one interception and two forced fumbles in three years with the Saints before Saturday.

The Saints will have a big decision to make this offseason about whether to keep Byrd or possibly work out a pay cut with him. He is due $7.8 million in salary and bonuses.

Last but not least, Saturday's victory was redemption for Brees. Two weeks ago in Tampa, Brees had his worst passer rating in four years (48.5). His passer rating was 104.9 on Saturday.

"The big emphasis for us the last two weeks has just been, 'Back to our standard,'" Brees said. "Back to our level of execution in both the run game and the pass game."