By Michael Hurley, CBS Boston

BOSTON (CBS) — Tom Brady entered this weekend having run for 24 touchdowns in his career in the regular season and postseason combined. Generally, though, there’s not much “running” involved in those plays, as most of them have come on quarterback sneaks and/or leaps over the center’s back with the football extended over the goal line.

So whenever Brady dusts off his track shoes and bursts for the end zone, it’s always going to make some headlines.

Brady did exactly that during Sunday night’s wild shootout at Gillette Stadium when he escaped a would-be sack from Breeland Speaks, ran toward the goal line and made a headfirst dive to put six points on the board for the Patriots.

It’s a play that Brady’s not known for making, and he admitted after the game that he wasn’t entirely in his element when it was happening.

“Yeah, I didn’t know what happened,” Brady said. “They doubled three guys on the play, and I’m just glad. You know, I’ve got to watch it tomorrow, but I got close to the goal line and figured I’d just try to get it in. We needed it.”

That they did, as every point proved to be extraordinarily valuable in this game, which the Patriots eventually won 43-40. Brady’s rushing touchdown put the Patriots ahead, 37-33, in the fourth quarter, after New England had fallen behind for the first time all night.

Head coach Bill Belichick expressed his gratitude for Brady’s willingness to pick up some hard-fought yards to score the touchdown.

“Obviously, Tom’s touchdown run was a big run. Not the guy you think you’re going to get that from, but he did a great job of getting the ball in the end zone there so we didn’t have to kick a field goal there,” Belichick said.

Running back James White, who’s usually the one scoring touchdowns like that, was impressed with what he saw from the 41-year-old quarterback.

“It was pretty impressive. He was pretty agile right there,” White said. “He does a great job when he gets the opportunity. It may not happen much, but he gets the job done running. If teams are going to drop eight in the red zone, that’s what it’s going to be sometimes.”

Though Speaks had Brady in his grasp, the rookie linebacker lost his grip on the quarterback, allowing Brady to scamper for the score.

“I don’t think Breeland is going to miss many of those,” Chiefs head coach Andy Reid said. “Tom is a big strong guy and he got himself out of it and made a play.”

Brady ended up engineering a game-winning drive a few minutes later, and he finished the night with 340 passing yards and one passing touchdown on 24-of-35 passing. He connected with seven different receivers, and five of them caught at least three passes.

“I think we have a lot of clutch players,” Brady said. “I think we have no problem grinding it out. That’s what the football season’s all about. I don’t think we’ve seen our best. I think we can all play a lot better, and I think that’s what we plan to do.”

It was a big night for Brady in terms of some career accomplishments, too. He won his 200th regular-season game, the most ever for a quarterback, and he won his 227th overall game, putting him one ahead of Colts kicker Adam Vinatieri for most all time by any player.

The Patriots improved to 4-2 with the win, while the Chiefs dropped to 5-1.