The Colts' defense, meanwhile, held Kansas City without a first down until late in the third quarter.
Manning completed 30 of 38 passes for 268 yards and -- after the Chiefs closed within eight points near the end of the third period -- he drove the Colts 71 yards in nine plays and hit Reggie Wayne with a five-yard scoring pass.
Joseph Addai contributed 122 yards on 25 carries for the Colts and scored on a six-yard run in the third period for a 16-0 lead.
Kansas City's offense was frustrated all day, barely reaching 150 total yards.
Even when Ty Law returned a first-half Manning interception inside the Indianapolis nine-yard line, the Chiefs had to settle for a field goal attempt that would have cut their deficit to 6-3. But Lawrence Tynes missed it.
Indianapolis will play in Baltimore next weekend in the division round. The winner of Sunday's New England-New York Jets game will take on San Diego next weekend.
Celebrity Families of 2014 [PHOTOS]