Bernard, a rookie out of North Carolina, gained 99 yards on 12 carries. Green-Ellis added 48 yards on 17 attempts, and the Bengals chewed up 155 yards on the ground overall.
The Colts also had a pair of young players step up on offense.
Second-year receiver LaVon Brazill and rookie Da'Rick Rogers caught two touchdown passes each as Indianapolis mounted a futile second-half rally.
Rogers, who finished with a team-high six receptions for 107 yards on nine targets, got the Colts on the board with a 69-yard catch and run at the 9:57 mark of the third quarter. Brazill, who caught three passes for 53 yards, followed a little more than three-and-a-half minutes later with a 19-yard catch-and-run on which he broke six tackles.
"I was running with anger there," Brazill said. "Da'Rick Rogers inspired me with his two touchdowns."
Those scores pulled Indianapolis within 21-14 with 6:20 remaining in the third quarter, but the Bengals answered with a 14-0 run to again put the contest out of reach.
Brazill added a 29-yard touchdown reception with 9:48 to play in the fourth quarter, and Rogers scored the game's final points on a 2-yard catch with 1:20 remaining.
Despite the loss, the Colts clinched their first AFC South championship since 2010 when Denver routed Tennessee later in the day.
"We never like to backdoor your way into the playoffs," outside linebacker Robert Mathis said. "You want to get momentum. Get things on the right track and keep things on the right track. I'm not going to sneeze at a division title."