Brady, who surpassed Hall of Famer Joe Montana with his 17th play-off win, completed 25-of-40 passes for 344 yards and three touchdowns in the divisional play-off, setting up a rematch of last year's AFC title game with the Baltimore Ravens.
"I grew up a 49ers fan, so Joe Montana and Steve Young were always my two favorites, but those two are in another class," Brady said.
"I'm glad to be a part of this organisation and to be a part of so many great teams. I've been very fortunate."
The Patriots, who will host Baltimore on Jan. 20, beat the Ravens 23-20 at home last year for the AFC title to earn their fifth berth in the Super Bowl since 2001.
Brady led a balanced attack spurred by the play of reserve running back Shane Vereen, who rushed for a touchdown and caught a pair of TD passes filling in for injured Danny Woodhead.
New England also had to do without tight end Rob Gronkowski, who broke his arm on Sunday, just two games back after breaking his forearm, and is expected to miss the rest of the play-offs.
The host Patriots blew open a game that was 17-13 at intermission, building a 38-13 lead early in the fourth quarter.
Houston mounted a frantic comeback that produced a pair of touchdowns passes to Devier Posey and Arian Foster to draw within 10 points at 38-28 with just over five minutes to play.
But the Patriots recovered an onside-kick and moved the ball into field goal range with kicker Stephen Gostkowski nailing his attempt from 38 yards to put the finishing touch on the victory.
Brady, winner of three Super Bowl rings with the Pats, kept Houston off balance with a hurry-up offense and quick snaps that froze the Texans in their defensive arrangement and caused some confusion at the line of scrimmage.
The Patriots, the league's highest-scoring team who routed the Texans 42-14 last month in a regular season game, got out to a 17-3 lead in the second quarter before the Texans rallied with 10 points in the last 75 seconds before halftime.
Houston quarterback Matt Schaub, playing catch-up in the second half, completed 34-of-51 for 343 yards with two touchdowns and one interception.
"It's very difficult when your season ends, no matter how it ends, unless you're the last team standing," Schaub said.
"We came in here and we battled. Guys fought tooth and nail all night long but they just made more plays than we did."
Running back Foster was held to 90 yards, though he scored one touchdown on the ground in addition to his TD reception.
After a short field goal by Houston following a 94-yard return of the opening kickoff by Danieal Manning, a one-yard scoring plunge by Vereen late in the first quarter gave the Patriots a lead they would never lose.
Brady followed a Patriots' field goal by hitting Vereen in the flat for an eight-yard touchdown pass that made it 17-3.
Foster, limited to 10 yards on six carries deep into the second quarter, erupted as the half drew to a close, ripping off runs of 21 and 19 yards on successive snaps before scoring from one yard out to close the gap before halftime.
A 40-yard pass to Aaron Hernandez set up an eight-yard TD run by Stevan Ridley on the first series of the second half and TD passes to Brandon Lloyd and Vereen put the game out of reach for the winners.
"Today was a big win for us," said New England coach Bill Belichick, who improved his play-offs record to 18-7. "The Texans are a good football team. They battled us to the very end.
"We had a bunch of guys step up today and make the plays that we needed to make. I'm happy for the players. They earned it."