Osweiler came into the game after starter Trevor Siemian left with reportedly a dislocated left shoulder after a sack in the first quarter. Osweiler completed 12 of 17 passes for 194 yards. Broncos running back C.J. Anderson gained 158 yards on 30 carries.
It was the fifth straight loss for the Colts (3-11). The Broncos (5-9) won their second in a row after snapping an eight-game slide.
After the Colts increased their halftime lead to 13-7 on a 39-yard field goal by Adam Vinatieri, the Broncos scored the final 18 points.
The Broncos took the lead on a 22-yard touchdown pass from Osweiler to Cody Latimer to take a 14-13 lead with 4:16 left in the third quarter.
After a three-and-out by the Colts, Osweiler completed a 54-yard touchdown pass to Jeff Heuerman and then a two-point conversion pass to Latimer to push the lead to 22-13 with 2:37 to go in the third quarter.
Denver boosted the lead to 25-13 on a 40-yard field goal by Brandon McManus with 5:13 remaining.
In the third quarter, the Colts lost linebackers Jeremiah George (neck) and Jon Bostic (knee), and right guard Denzelle Good left with a knee injury.
The Colts led 10-7 lead at halftime.
Kenny Moore II made his first career interception on the Broncos' first possession, picking off Siemian and returning it 25 yards to the 50. The Colts scored on a third-and-2 from the 7 as Brissett scrambled up the middle for 7-yard touchdown run to put the Colts up 7-0.
The Broncos drove to the Colts 7 before things broke down. After two incomplete passes, Siemian was injured on a sack by linebacker Barkevious Mingo and was forced to leave the game. Following a delay of game penalty, McManus missed a 40-yard field goal attempt with 1:30 left in the opening quarter.
Osweiler replaced Siemian on the next possession.
The Colts drove 59 yards in 10 plays before settling for Vinatieri's 45-yard field goal in the second quarter.
On the ensuing possession, the Broncos went 75 yards on 11 plays. A 30-yard touchdown pass from Osweiler to Devontae Booker, who cleanly hurdled a defender, was wiped out by an offensive holding penalty. Osweiler, who had completions of 22 and 17 yards on the drive, eventually scored on an 18-yard scramble up the middle.
NOTES: Colts TE Brandon Williams was hurt on a Colts' punt in the first minute of the second quarter and was carted off the field in a stretcher with a head injury. Williams had movement and there was no neck injury. He was strapped in as a precaution. ... Colts C Ryan Kelly missed his third consecutive game with a concussion. Kelly was replaced by Mike Person. ... WR Chester Rogers started in place of Donte Moncrief, who was out for the second game in a row with an ankle injury. ... The Broncos put SS Justin Simmons on injured reserve. Simmons was injured while celebrating Brandon Marshall's strip-sack of Jets quarterback Josh McCown in Sunday's 23-0 shutout by Denver. Will Parks started in Simmons' place.