NEW ORLEANS — There’s a saying about teams in the Saints’ situation this time of year: “You can either keep playing or go Christmas shopping.”

The Saints chose to do the former Sunday. And with an opponent that apparently chose to do the latter, they’ll be going to Dallas next Sunday with at least a glimmer of playoff hope.

“We’ve got a football team that’s full of a lot of guys with pride and a lot of guys with want-to,” interim coach Joe Vitt said after his team’s 41-0 victory against Tampa Bay. “They’re accountable to each other. It was gratifying to be part of today’s game.”

This was the same guy who a week earlier was calling the same team “fragile” after its 52-27 whipping at New York, citing a “here we go again” mindset when adversity strikes, which it had often in a three-game losing streak that pushed the Saints to the brink of playoff elimination.

And there was more adversity during the week when right tackle Zach Strief and safety Malcolm Jenkins, whose tackle of Vincent Jackson saved the Saints’ victory in the teams’ first game, went down with injuries — Jenkins for the season.

“Once we got back to work on Monday and analyzed the situation we were in, we know we had two ways to go,” said safety Jabari Greer, who had the first two-interception game in his nine-year career. “We decided to play Saints football.”

So, as it turned out, the ones who were fragile Sunday were the Buccaneers, who also had lost three straight, and the fans, who at best filled the Mercedes-Benz Superdome to two-thirds of its capacity.

Oh ye of little faith.

A near-flawless 74-yard touchdown drive on the opening series set the tone for a day when the Saints were in command from start to finish.

“We knew we had a good game plan coming in,” guard Jahri Evans said. “And when we moved the ball down the field like we did on that first series, we knew it was going to be a good day.”

It also helped that the adversity was minimal. But that’s generally what happens when you’re playing a team that lost its mojo in last week’s 23-21 loss to Philadelphia.

Bucs quarterback Josh Freeman, who threw for 420 yards against the Saints the first time around, looked like Morgan Freeman.

But credit is due a Saints defense that has quietly gotten better despite the losing streak and posted the franchise’s first shutout since 1995.

And credit Drew Brees, who’d be the first to admit he hadn’t justified his richest-in-the-NFL contract during that span, plus his offensive colleagues for a turnover-free, 447-yard effort.

Sunday’s victory, as impressive as it was, did feel a little hollow because of all that’s gone on before it. It probably won’t be enough to extend the season past the Carolina game Dec. 30.

Vitt acknowledged that.

“We won a game today, and now we’ve got to prepare for Dallas,” he said. “We’re not spiking the ball.”