But Denver safety Justin Simmons blocked the kick and defensive back Will Parks scooped up the ball and returned it the other way for 2 points to give the Broncos a 25-23 lead.
The play was reviewed to see if Parks had stepped out of bounds during the return, but the call stood and the Broncos left the Superdome with the win.
MORE: Broncos-Saints highlights, stats
The Saints (4-5) have a quick turnaround before heading to Charlotte for a Thursday game against the Carolina Panthers, who fell to 3-6 following their own loss filled with late-game drama. Panthers receiver Kelvin Benjamin was stripped by Kansas City Chiefs cornerback Marcus Peters to set up a game-winning 37-yard field goal by Cairo Santos.
The Chiefs (7-2) moved into a tie with the Oakland Raiders atop the AFC West, while the Tampa Bay Buccaneers (4-5) were the only team in the NFC South to win Sunday.
