In a game of wild ebbs and flows Sunday at the Mercedes-Benz Superdome, Tampa Bay Buccaneers cornerback Johnathan Banks unwittingly provided a huge helping hand in overtime to the victorious New Orleans Saints.

Make that two helping hands.

A crucial illegal use of hands penalty against Banks on third-and-10 in the first minute of overtime enabled the Saints to retain possession and ultimately defeat the Buccaneers 37-31 on Khiry Robinson’s dramatic 18-yard touchdown run at the 9:24 mark.

Robinson’s run to glory capped a determined 12-play, 80-yard scoring drive that extended the Saints home winning streak to 19 games with coach Sean Payton on the sideline.

Banks’ penalty was the last of 15 infractions called against the Buccaneers resulting in minus 113 yards. It negated an incomplete pass thrown by Saints quarterback Drew Brees on the opposite side of the field from where the penalty occurred and gave a new set of downs to the home team.

“I don’t feel like I hit (the Saints receiver) in the face,’’ Banks said. “But the refs made the call, and you got to live with it. I thought we (were) off the field. I didn’t see the penalty until I saw the refs running toward the huddle and I thought, ‘what now?’ We still had a chance to go out and make something happen and we didn’t. We lost. It’s on me.’’

In a game of 140 plays from scrimmage, Banks’ penalty did not decide the outcome in and of itself. But it seemed to capsulize the struggles of a 1-4 team under first-year coach Lovie Smith that was playing its third consecutive road game against quality competition.

In Weeks 3 and 4, Tampa Bay got blown out by the Atlanta Falcons 56-14 and rallied to upset the Pittsburgh Steelers 27-24 in the waning seconds.

“This was a key game for us,’’ Smith said. “We put a big emphasis on it — on the road, a division game; that in itself says quite a bit. For us to be able to steal one would have put us in a pretty good position. We had our opportunities to finish, but I’m disappointed in the way we finished.’’

The Bucs rallied from a 13-0 hole after 20 minutes with 24 consecutive points in the second and third quarters behind second-year quarterback Mike Glennon and a 33-yard interception return for a touchdown by linebacker Danny Lansanah.

The Bucs led 31-20 with 13:28 remaining after Glennon’s second touchdown pass. But the Saints pulled even with a 27-yard touchdown run by Pierre Thomas, a safety by outside linebacker Junior Galette and a 44-yard field goal by kicker Shayne Graham to send the game to overtime.

“Whether we lost it or whether they won it, they went out and took it from us,’’ said Buccaneers linebacker Jonathan Casillas, who played with the Saints in 2009 and 2011-12. We had it in our hands, and they took it from us. We got to find a way to finish and win games like this. We had ’em down; we got to keep ’em down.’’

Smith agreed.

“We had our chances,’’ he said. “We did some good things; we just didn’t do enough of them. This was a game we could have won. Eventually, we’ll figure out how to win.’’