It was the first NFL playoff game without a touchdown in 27 years.
"This was as hostile an environment as I've ever played in," said Indianapolis quarterback Peyton Manning. "I can't say enough about our team."
Manning completed 15 of 30 passes for a modest 170 yards with two interceptions, but he moved the Colts enough to get into Vinatieri's range.
The Indianapolis kicker was good from 23 and 42 yards in the first period, 51 yards in the second quarter, 48 yards in the third and 47 yards with 23 seconds left in the game. Baltimore's Matt Stover kicked field goals of 40 and 51 yards.
Indianapolis will play for the AFC championship next weekend against the winner of Sunday's New England-San Diego game. If New England is the winner, the Colts will have the home field for the AFC title contest.
It will be the second conference championship appearance for Manning in his nine-year career. He has yet to reach the Super Bowl.