Coming off a first-round bye and playing at Gillette Stadium where they have not lost all season, the Patriots kept their perfect home record intact and now await the winner between the top-seeded Denver Broncos and San Diego Chargers, who clash on Sunday in the other AFC divisional playoff.
The Patriots have traditionally relied on the arm of future Hall of Fame quarterback Tom Brady to get the job done but used a punishing ground game to subdue the Colts on Saturday.
Blount led the charge, rushing for a New England playoff record 166 yards and powering his way into the end zone for four scores, including a 73-yard rumble, with Stevan Ridley running in two more.
Brady, who has thrown 42 career post-season touchdown passes to sit third on the NFL all-time list, completed just 13-of-25 pass attempts for 198 yards and no touchdowns.
"We've been doing a good job at that (running the ball) since Thanksgiving really, we've been a great running team," said Brady after notching his 18th career post-season win, the most by any NFL quarterback.
"Our offensive line, what they did tonight, the way our backs ran was awesome.
"It was amazing, just keep handing it off and those guys keep running so hard and do such a great job finding the holes, slicing through there and finding as many yards as they can."
The Colts, who rallied from a 28-point deficit to beat the Kansas City Chiefs a week earlier in a wild card contest, once again found themselves playing catch-up as the Patriots bolted to a 14-0 lead.
Four times this season the Colts erased double-digit deficits and rallied for wins but they could not find a way back against the Patriots.
Colts quarterback Andrew Luck, intercepted only nine times through the regular season, was picked off four times by the Patriots, the first by Alfonzo Dennard who returned the ball to the Indianapolis two yard line.
Blount bullied his way into the end zone with just 79 seconds gone in the game.
On New England's next possession, Brady engineered a clinical 74-yard drive that was capped off with Blount driving over for the touchdown as the rain-soaked home crowd erupted in wild celebration.
"We tried hard but we just couldn't get over that hump," said Luck, who tossed seven interceptions in two playoff games.
"This is not a good feeling right now, it will take a while to go away.
"We just couldn't get a rhythm going early and the first series interception put our defense in that position, it's inexcusable and that's on me."
The never-say-die Colts hit back in spectacular style with Luck firing a 38-yard strike to a streaking LaVon Brazill but the Patriots quickly restored their two touchdown cushion when Blount capped off another drive with a two-yard plunge.
Indianapolis began to chip away at the New England lead in the second quarter, Adam Vinatieri booting a 36-yard field goal before adding a safety when the snap sailed over Patriots punter Ryan Allen's head and knocked through the end zone to send the Colts into the break trailing 21-12.
A Vinatieri 21-yarder to open the second half scoring trimmed the Patriots' lead to 21-15 but again New England answered with a long drive and Ridley getting the score.
Before the end of the third quarter Luck again went back to Brazill for a 35-yard touchdown to get to within a touchdown at 29-22.
But that would be as close as the Colts would get as the Patriots dominated the final quarter, Blount racing 73-yards for a touchdown and Ridley diving over from the one for another.
"The plan is always to move the ball and score points, so whatever is the best way to do that, that's what we're going to do," said Patriots head coach Bill Belichick, who picked up his 19th career playoff win to move into second place on the all-time list.
"We got off to good start and were able to play from ahead."
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- Stevan Ridley