After a wild fourth quarter that featured a blocked field goal, a fumble and an interception, Cousins and the Falcons (3-2) got the ball back at their own 20 with 1:14 remaining in regulation and no timeouts, trailing 30-27.
Cousins completed five passes to push Atlanta to the Buccaneers 29, then hustled to the line to spike the ball with a single second left.
In all the confusion, the Falcons were called for delay of game as they lined up for a tying field goal, but it didn’t cost them.
Younghoe Koo knocked it through from 52 yards to force overtime, one week after he made a 58-yarder with two seconds left to beat the New Orleans Saints.
The Falcons won the coin toss in overtime and made sure Baker Mayfield and the Buccaneers (3-2) didn’t get their hands on the ball again.
Cousins connected with Drake London on a couple of passes before throwing a short one to Hodge, who broke a tackle at the 40, sliced through a gap in the secondary and raced untouched to the end zone to end the game.
The four TD passes tied Cousins’ career best, while his yardage through the air easily eclipsed his previous high of 460 with the Minnesota Vikings in 2022.
After signing his big free agent deal with the Falcons, which included $100m in guaranteed money, the 36-year-old Cousins got off to sluggish start in Atlanta.
But on Thursday he broke Matt Ryan’s Falcons record for passing yards in a game (503) with one of the most prolific performances in NFL history.
Only 14 quarterbacks have thrown for more yards in a game, led by Norm Van Brocklin’s mark of 554 yards that has stood since 1951.