Their third-string quarterback/read-option specialist/WR/TE/RB/kickoff returner/special teams ace came up with the first blocked punt of his career. And it couldn't have come at a better time.
The Saints were trailing 14-3 in the third quarter at the Tampa Bay Buccaneers on Sunday, staring their second straight loss in the face, when Hill's block finally woke them from their slumber.
They outscored Tampa Bay 25-0 after that to run away with a 28-14 victory -- and officially secure their second straight division title for the first time in franchise history.
The Saints (11-2) got to enjoy a proper celebration in Tampa's visiting locker room. More importantly, they have rediscovered their momentum after a 13-10 loss at Dallas last week and continued a battle with the Los Angeles Rams for the NFC's No. 1 seed.
"You call those momentum-changing plays, right?" said Drew Brees, who had two turnovers in a game for the first time all season before the late surge (an interception in the second quarter and a sack/fumble in the third quarter). "We all recognize when you have those games where you're struggling to get something going, you just need one thing to just ignite the team, ignite the sideline, and get you going.
"Obviously that was a huge play in the game. We go down and score a touchdown and score on every possession after that, I think.
"It was the epitome of a great team win."
The Saints did not bring any extra rushers on the punt block, but Hill said special teams coordinator Mike Westhoff gives players the freedom to attack when they see an opportunity. And Hill said both he and defensive end Alex Okafor saw the same opening.
"And, man, [Okafor] draws so much attention that he took both the win and the tackle, and I got there pretty early," Hill said. "My whole thing was just, 'Don't miss the ball' because I got there so early."
Hill, who had never blocked a punt at any level of football, also credited Westhoff for foreshadowing the game-changing play.
"I remember sitting on the bench next to Coach Westhoff and he said something to me like, 'Man, I've been a part of football for a long time, and this is the type of game where we as a special teams unit need to make a big play to change the momentum here,'" Hill said. "That was our mindset as a special teams unit, and that's what we were hoping for."
Hill has been a revelation for the Saints this season as his role has grown on offense and special teams. Brees recently called him Sean Payton's "new toy."
But he went back to his "roots" for his biggest play of the season to date. Hill first got on the field last season as a special teams coverage specialist when the Saints wanted to find a way to get their athletic undrafted rookie onto the field. And he has had several nearly blocked punts in the meantime before he finally broke through up the middle Sunday.
The 6-foot-2, 221-pounder, who was nicknamed a "Thor-terback" by former BYU coach Bronco Mendenhall, has now run for a TD, converted two fake punts (one throwing, one running) and caught two passes this season, among other achievements.
"He wants to play hard because he loves the game, and you feel that," said Payton, who has long described Hill as having an "infectious" quality. "I think he's very unselfish, and that carries over because it's contagious. ... There's just some of those intangibles that he's willing to do anything -- but do it well.
"So he's a very important part of our team."
Before Hill woke them up, New Orleans' stunning offensive slump lasted more than six quarters -- starting in Dallas on Thursday night in Week 13 and continuing on a wet, sloppy field in Tampa.
Then suddenly everything changed. Ingram ran for 11 yards on the very next play and finished with 13 carries for 52 rushing yards and a touchdown. Brees threw a TD pass to fullback Zach Line four plays later and later leaped for a 1-yard TD run when the Saints went for it on fourth-and-goal.
Kamara finished with 87 yards from scrimmage. Michael Thomas caught 11 passes for 98 yards (giving him a whopping 27 catches against Tampa Bay this season).
And the Saints' defense started to have its way with Tampa Bay with three sacks in the second half. Defensive end Cameron Jordan finished with two sacks for the third straight game. Linebacker A.J. Klein and defensive tackle Sheldon Rankins also got in on the fun with one sack each.
Jordan called the 25-0 run a "tidal wave."
"It was kind of two different games really," said Payton, who credited both the blocked punt and the way the defense played throughout the day to allow New Orleans to "hang in there."
"To be able to win a game maybe where you didn't play your best in one certain area or another was significant," Payton said.
The Saints added one last exclamation point when cornerback Marshon Lattimore made a fantastic toe-tapping interception in the end zone with one second left -- allowing him to one-up Buccaneers receiver Mike Evans in their growing rivalry.
Evans caught a pass for 36 yards behind Lattimore on Tampa Bay's opening touchdown drive but was held mostly in check after that, finishing with four catches for 86 yards.
The Saints will now shift to another division rival, playing at the slumping Carolina Panthers on Monday Night Football in Week 15, before playing host to the Pittsburgh Steelers and Carolina again to wrap up the regular season.