FOXBOROUGH, Mass. — The New England Patriots have accomplished so much under Coach Bill Belichick and quarterback Tom Brady, but they found something new to achieve on Saturday night at Gillette Stadium. In outlasting the Houston Texans, 34-16, the Patriots set an N.F.L. record for conference dominance and used a rare performance by a running back to get it.
The Patriots became the first team in the Super Bowl era to reach the conference championship game six years in a row. And running back Dion Lewis became the first player to score touchdowns on a run, a reception and a kickoff return in a postseason game.
It was enough to turn a tight game into another January rout, as the Patriots have done for years in the divisional round. In the previous five seasons, New England won each of its games at this stage in the postseason, all at home, by an average of 16 points. Accordingly, they were 16-point favorites to win on Saturday, the largest spread for any playoff game since 1998.
Houston, meanwhile, had never survived this round and had gotten here by beating an Oakland Raiders team that was forced to start its third-string quarterback. The last time the Texans played in New England, the Patriots shut them out behind quarterback Jacoby Brissett. He was inactive on Saturday.
The starter this time, of course, was Brady, who missed the first game with the Texans while serving a suspension related to the deflation of footballs here during the 2015 A.F.C. championship game.
Brady was coming off a remarkable regular season, averaging nearly 300 passing yards per game, with 28 touchdowns and two interceptions. He matched that interception total on Saturday, but in the end, it did not matter much.
Brady threw his first touchdown pass with 9 minutes 27 seconds left in the first quarter, finding Lewis for 13 yards. The Texans then turned an unsportsmanlike conduct penalty on Eric Rowe into a sustained drive, collecting four first downs but settling for a Nick Novak field goal to make it 7-3.
Novak’s ensuing kickoff fell to Lewis at the 2-yard line, but Lewis tore through the Texans, eluding a diving Robert Nelson and dashing untouched into the end zone. It was the first postseason kickoff return for a touchdown in Patriots history and the second score of the quarter for Lewis, who had no touchdowns in the regular season.
At that point, the Texans probably needed something strange to happen, and the Patriots provided it. Brady’s first pass of the second quarter bounced off the fingers of wide receiver Michael Floyd and into the arms of cornerback A. J. Bouye. Again, the Texans could manage just a field goal, to make it 14-6.
And again, the Patriots would help them out.
This time, Lewis’s kickoff return went as poorly as possible. Akeem Dent forced a fumble, and the Texans recovered at the New England 12-yard line. Two plays later, Houston quarterback Brock Osweiler found tight end C. J. Fiedorowicz for a 10-yard touchdown strike.
The fans had reason to expect a blowout, but with the Patriots’ lead cut to 14-13, they went quiet. The next two drives brought more cause for concern: Both ended with a sack and a punt. Even the Patriots’ last drive of the half was unfulfilling, ending with a field goal after three plays from inside the 5-yard line.
On the Patriots’ second drive of the third quarter, though, Brady connected four times with Julian Edelman, who finished with 137 yards and moved into eighth on the list for postseason receptions in a career. The drive ended with a 19-yard touchdown pass to James White, and New England carried the 24-13 advantage into the fourth quarter.
Yet, after five seconds, Novak knocked through a 46-yard field goal, capitalizing on Andre Hal’s interception of Brady late in the third quarter. Novak’s kick made it a one-score game, at 24-16, but the Patriots’ defense soon soothed any anxiety the crowd might have felt.
With 13 minutes left in the fourth quarter, Osweiler fired to DeAndre Hopkins, who tipped the ball to Logan Ryan for an interception. Ryan returned it 23 yards to the Texans’ 6-yard line, a devastating blow for Houston. Two plays later, Lewis rumbled into the end zone from 1 yard out.
Lewis, who was playing in his first career postseason game, had scored three touchdowns: one receiving, one on a kickoff and one rushing. The last player to do that in a game was Kansas City’s Tyreek Hill this season, and before that, Chicago’s Gale Sayers in 1965.
An earlier version of this article misattributed a distinction to Dion Lewis. He scored three touchdowns Saturday, one receiving, one on a kickoff and one rushing, but he was not the third player in N.F.L. history to do so.