NEW ORLEANS — In a search for evidence that things could get better — quickly — coach Sean Payton and the New Orleans Saints had to look no further than their next opponent.

The Tampa Bay Buccaneers, who visit New Orleans on Sunday, looked like a lost cause during a humiliating, mistake-filled 56-14 pummeling at the hands of the Atlanta Falcons in a Thursday night game to open Week 3.

They responded in Week 4 with a stirring 27-24 comeback victory at Pittsburgh.

So as the Saints got back to work after their own prime-time embarrassment — a 38-17 loss at Dallas last Sunday night — they were comforted, somewhat, by Tampa Bay’s example of how fast fortunes can change in the NFL.

“At times in this league, scores can be overrated. No one wants to get blown out ... but you don’t want to see a score and jump to conclusions,” Saints center Jonathan Goodwin said.

“In this league, everybody’s good, everybody’s capable of winning. It’s just about getting in that groove where you’re doing way more things right than you’re doing wrong.”

Payton pointed out that while Tampa Bay is 1-3, the Buccaneers have been competitive in 75 percent of their games.

“If you look at their three losses, one of them obviously was a big differential but the other two weren’t,” Payton said. “They played some pretty close games to start the year and just didn’t come up on the winning end.”

That’ll sound familiar to Saints fans. New Orleans (1-3) had leads in the final 10 seconds of each of its first two road games, only to lose both by a field goal or fewer.

The Saints broke into the win column with a 20-9 victory over undermanned Minnesota in Week 3 before falling flat in Dallas.

Fortunately for New Orleans and Tampa Bay, no one is showing signs of separating themselves in the NFC South. Carolina and Atlanta both lost last week to fall to 2-2, meaning the Saints and Bucs are just one game out of first place with 12 games left, despite their disappointing starts.

“This week is a big week for both us and New Orleans,” Bucs quarterback Mike Glennon said. “Whoever wins will be 2-3 and could end up at the end of week being tied for first place in the division.”

Wrecked Ryan

Defensive coordinator Rob Ryan was celebrated like a hero during his first season in New Orleans. His second hasn’t gone so well. The Saints defense, which finished 2013 ranked fourth in the NFL, ranks 29th through the first four games this season. They’re allowing 396 yards per game, 90 more yards, on average, than last season. New Orleans is struggling to get pressure on quarterbacks, with only five sacks so far, and turnovers have been hard to come by as well, with no interceptions and one fumble recovery.

Timely return

With Bucs rookie wide receiver Mike Evans’ status up in the air because of a groin injury, Louis Murphy could play a key role. Murphy, who also played for Oakland, Carolina and the New York Giants during a six-year career, was released after the final preseason game but re-signed on Sept. 28. Five days later, he had six catches for 99 yards in his Tampa Bay debut at Pittsburgh, including a 41-yarder that to set up Glennon’s game-winning TD pass to Vincent Jackson.

Good Cooks

One area in which the Saints continue to be exceptional is the passing game, which has been aided by the addition of first-round pick Brandon Cooks. His 23 catches lead all rookies. He has 199 yards and one TD receiving.

“He’s been really productive,” quarterback Drew Brees said. “We can line him up all over the field.”

Cooks, along with star tight end Jimmy Graham, are the main reasons Brees ranks third in the NFL with 1,203 yards passing.

Rejuvenated D line

Improving the pass rush was one of Tampa Bay’s top priorities during the offseason, and Bucs coach Lovie Smith is beginning to get some results for the effort. In addition to Pro Bowl tackle Gerald McCoy returning to the lineup after missing one game because of a broken left hand, the team’s big catch in free agency — end Michael Johnson — also played a key role last week after sitting two weeks with an injured ankle.

The tandem set the tone for the defense against the Steelers, sacking Ben Roethlisberger on the first two plays, with Johnson forcing a fumble that led to an early touchdown. Another lineman slowed by injury, Da’Quan Bowers also had one of the team’s five sacks of Roethlisberger.

Home cooking

While the Saints have started the season 0-3 on the road, they’ll be looking for their 19th straight win in the Superdome, including playoffs, with coach Sean Payton on the sideline (Payton was suspended in 2012). The last team to beat Payton in the Superdome? Tampa Bay, on the final day of the 2010 regular season.

AP sportswriter Fred Goodall in Tampa, Florida, contributed to this report.