Boldin set a new franchise record with 145 yards receiving, including a fourth-quarter touchdown, in what turned out to be a one-sided contest.
The result takes Baltimore through to a play-off with AFC West champions the Denver Broncos next weekend.
It was a disappointing end to an impressive run of form from the Colts, who had made it through to the wild card game just one season after finishing with a league-worst 2-14 record.
The Seattle Seahawks overcame a 14-0 first-quarter deficit to claim a 24-14 win in the NFC wild-card game against the Washington Redskins, whose miserable day was topped off by a knee injury to quarterback Robert Griffin III.
The match started well for Griffin who, playing in his first play-off game, threw two touchdown passes in the first quarter, to Evan Royster and Logan Paulsen, to put his side in control.
But Russell Wilson threw a touchdown pass to Michael Robinson and Steve Hauschka kicked two field goals in the second to put the Seahawks within one.
In the fourth, Marshawn Lynch scored on a 27-yard run to put Seattle ahead, before Griffin - who had earlier stayed in the game after an awkward fall - injured his right knee for the second time in a month, and the Seahawks added another field goal.
The Seahawks will go on to face the Atlanta Falcons.