Patriots running back Shane Vereen is congratulated by quarterback Tom Brady after a touchdown reception in the second quarter. (Elise Amendola/Associated Press)

When Tom Brady completed a nice little five-yard pass to Brandon Lloyd for the touchdown that essentially ended a wild weekend of NFL playoffs, he turned to his sideline, where his New England Patriots celebrated, and walked calmly toward the bench. He accepted congratulations as he grabbed a seat. Once there, he barked at his offensive teammates, clipboard in hand.

This was Brady, the pilot of what amounts to one of the best offenses in NFL history, at work. He sucked the drama out of one of the most dramatic playoff weekends ever with unforgiving precision, leading the Patriots to a 41-28 victory over the Houston Texans, who endured a power-point presentation at Brady’s office.

Brady’s performance against the Texans, in which he completed 25 of 40 passes for 344 yards and three touchdowns, assured that the Patriots will host the Baltimore Ravens in the AFC championship game for the second year in a row. It kept alive the pursuit of Brady and Coach Bill Belichick, who now fit into the New England landscape like a lobster roll and a cup of chowder, for a fourth Super Bowl title.

And it put the remaining three contenders for that title on notice: Brady, and this offense, might fade into the background during the season while the league concentrates on Peyton Manning or Robert Griffin III. But it is January, and that offense is still playing, and it is lethal.

This version, the 10th Brady and Belichick have brought to the playoffs, showed its versatility Sunday. Running back Danny Woodhead suffered a hand injury on New England’s first possession. Woodhead’s snaps, then, went to second-year back Shane Vereen. Vereen’s contributions: 124 total yards and three touchdowns, including the 33-yard pass that made it 38-13 early in the fourth quarter.

The Patriots’ offense missed, at various points this year, tight ends Rob Gronkowski and Aaron Hernandez. It still does not have a household name of a running back. Pro Bowl linemen have retired. And their most prolific wide receiver stands 5-feet-9 and was released by San Diego and held in such low regard by Miami that the Dolphins traded him, within their own division, to New England.

Yet these Patriots came into these playoffs supremely confident. They set an NFL record by recording 444 first downs. They led the league in scoring with 557 points, the third-highest total in history. They did that because they were the best team in the league on third down, and they were remarkably efficient in the red zone, with 67 touchdowns. Only three teams have ever had more. They averaged 427.9 yards per game; nine teams weren’t within 100 yards of that.

So when Brady started pushing buttons and pulling levers Sunday, the Gillette Stadium crowd had every right to believe it was in for another playoff treat. There is no gear into which Brady can’t slide this offense, which racked up 457 yards on Sunday. He can huddle up his guys and take his time. He can sprint to the line of scrimmage and not allow the opponent to breathe.

When Brady set the Patriots off on their first scoring drive Sunday, one which ended on a one-yard run by Vereen, Gronkowski was on the sideline, dealing with what appeared to be a problem with the left arm he broke earlier in the season. He never returned. Brady was unfazed. He hit three different receivers on that drive, in which he worked behind center and from the shotgun. The Texans reeled.

On the Patriots’ second touchdown drive, Brady concentrated on his favorite target, Wes Welker, that one-time castoff in San Diego and Miami. In the Patriots’ 42-14 pasting of Houston Dec. 10 — a Monday night embarrassment for the Texans, who wanted to consider themselves in the conversation as the AFC’s best team — Welker caught only three balls. Did that mean the Texans were unaware of the 115 others he caught throughout the season?

Welker’s sixth catch of the first half went for 47 yards, and on the next play, Brady found Vereen on a screen. He waltzed in from eight yards out, and New England — sometimes a Ferrari, sometimes a bulldozer — built a comfortable 17-3 lead.

Only an odd series of events just before the half put New England’s whole operation on hold. First, Houston returner Danieal Manning had his second long return, and a penalty gave the Texans the ball in New England territory. Arian Foster, Houston’s stalwart back, then used just two carries to cover 40 yards, and his one-yard touchdown run pulled the Texans within 17-10.

That might not have been unsettling to the Foxboro faithful had Brady managed to kill the final 75 seconds of the half. Brady threw incomplete passes on second and third downs and Houston forced a punt. On the half’s last play, Houston’s Shayne Graham knocked through a 55-yard field goal, the longest of his career, and the Patriots’ dominance had been deleted. They led just 17-13.

But that only set up the second half. The Patriots’ first drive, on which Brady completed four straight passes, ended in Stevan Ridley’s touchdown run. Their third drive, on which Brady went 3 for 3, ended with the touchdown pass to Lloyd. The lead was 31-13, and it grew to 38-13 on Vereen’s final score.

The Texans managed a pair of late touchdowns, but the histrionics that played out over the weekend in Denver, San Francisco and Atlanta would not resurface here. Tom Brady is back in the playoffs. He has his clipboard. He has his focus. He is back at work.