Blount set a New England post-season record with the 24-carry performance, which included a 73-yard TD run early in the fourth quarter for a 36-22 Patriots lead.
Stevan Ridley compiled 52 yards with two scores on 14 rushing tries as the Patriots rolled up 13 first downs on the ground amid wind and rain, advancing to their third consecutive AFC Championship game.
They will face the winner of Sunday's other AFC divisional round contest between Denver and San Diego.
Tom Brady completed 13-of-25 pass attempts for 198 yards in reaching the conference title game for the eighth time in his 12-year career.
Andrew Luck made good on 20-of-41 passes for 331 yards with two scores but was intercepted four times for the Colts.
T.Y. Hilton had four catches for 103 yards.