In the fourth quarter, Greer outran receiver Tiquan Underwood along the sideline to pick off Freeman's deep pass to the end zone.
In between, the rest of New Orleans' defense did about everything right to secure the franchise's first shutout in 17 years, while Drew Brees and the Saints' offense made their share of big plays in a 41-0 rout of the Tampa Bay on Sunday, eliminating the Buccaneers from playoff contention.
What was easily New Orleans' most complete performance of the season probably came too late, with the Saints (6-8) needing to win out and needing four teams to lose their last two games to sneak into the last NFC wild card spot. Yet, for Greer, playoff possibilities were beside the point.
"We are accountable to one another and no matter what situation we're in, we're going to band together," Greer said. "We were going to play for the men in our locker room and the fleur-de-lis on our helmet, and that's what we did."
New Orleans' defense produced five turnovers in all, four on interceptions of Freeman and one on defensive end Cameron Jordan's strip and recovery on his sack of Freeman.
The fans who stayed in the Superdome until the end got an additional moment to celebrate as the Saints stopped Tampa Bay one last time at the New Orleans 10, preserving the club's first shutout since a 12-0 win in the 1995 season finale against the Jets in New York.
The shutout meant a lot to a unit that came in ranked last in the league, in large part because of high yardage totals allowed early in the season while adjusting to the scheme of new defensive coordinator Steve Spagnuolo.
"We've come a long way. Our defense the first four or five games was on pace to be one of the worst defenses ever," Saints linebacker Jonathan Casillas said. "It's just good to finally get a game to where we can be like, 'All right, defense. This is us. This is what we're really all about.'"
The Saints' offense also looked more like the unit that set a slew of records last season.
Brees passed for 307 yards and four touchdowns. He avoided an interception for the first time in three games and connected on his scoring passes with tight end David Thomas, running back Darren Sproles and receivers Lance Moore and Joe Morgan. Mark Ingram added an 11-yard touchdown run.
"Even though maybe that Super Bowl trophy can't be ours this year, we still have a lot to play for," Brees said. "We have a very prideful group of guys, but also we have a group of guys that understand the big picture, and that is that we're going to be together for a long time and we can start building the foundation of something now that will carry over for years to come."
Freeman by contrast, was pulled in the fourth quarter with the game out of reach.
"It's my job to make sure everybody is educated as to what the play is. I've got to do a better job," Freeman said. "Some of those turnovers were really odd. Chalk it up to miscommunication."
Rafael Bush intercepted a pass thrown directly at him at the New Orleans 9, returning it 40 yards to set up a Saints touchdown drive. Isa Abdul-Quddus intercepted a long pass that Freeman seemingly threw up for grabs.
New Orleans also bottled up standout rookie running back Doug Martin, holding him to 16 yards on nine carries as the Buccaneers lost for the fourth straight time and suffered by far their most lopsided drubbing this season.
"We got our butts whipped, and that's it," Bucs guard Donald Penn said . "You can't sugarcoat it. We didn't perform today, and it's really tough and frustrating because we have so much talent."
The Saints will still be alive for a playoff berth when they kick off at Dallas next Sunday, but will have to finish in a multi-team tie at 8-8, which would require several other teams to lose their last two games. While the Bucs could finish 8-8, they would lose all possible tiebreakers.
Brees had been intercepted nine times during New Orleans' recent three-game skid. That he would rebound well against Tampa Bay made sense; the Bucs came in giving up a league-worst 311.6 yards per game. Brees eclipsed 200 yards by halftime but eased off after his 34-yard touchdown to Morgan in the second half.
Brees finished with more than 300 yards passing and four TDs for the 17th time in his career, passing Dan Marino (16) for the most times in NFL history.
Ingram finished with 90 yards rushing and the Saints had their third-best total on the ground this season with 149 yards against a Tampa Bay rushing defense that came in first in the league, allowing 78.2 yards per game.
NOTES: The Saints had a halftime presentation for former left tackle Willie Roaf, who last summer became only the second Saints player inducted in the Pro Football Hall of Fame in Canton, Ohio. Roaf was given the customary Hall of Fame ring as he stood behind his bronze bust, which will be returned to Canton. The only other Saints Hall of Famer is linebacker Rickey Jackson, inducted in 2010. ... The Bucs were shut out for the first time since Sept. 27, 2009, against the New York Giants.