FOXBOROUGH, Mass. -- Sam Bradford passed his first test as a starting quarterback in the NFL.

And the player who ended the game at that position for the Rams, Keith Null, directed a drive that set up Josh Brown's 37-yard field goal on the final play that gave St. Louis a 36-35 exhibition win over the New England Patriots on Thursday night.

Bradford, the top pick in this year's draft, was poised and precise in playing the first half. He went 15 of 22 for 189 yards after struggling as a backup in his first two games. But Tom Brady threw touchdown passes on three consecutive drives and the Patriots (2-1) turned a 27-14 deficit into a 35-27 lead.

St. Louis (2-1) rallied for a 2-yard touchdown run by Keith Toston and the game-winning field goal.

The Patriots didn't get a first down until 3:10 remained in the first half, but Brady finished with 18 completions in 22 attempts for 273 yards.

Bradford, the 2008 Heisman Trophy winner who missed most of last season at Oklahoma with a shoulder injury, had a much better half. He completed his first six passes and threw for two touchdowns in his first start since last October.

He went 4 of 4 for 48 yards and a 5-yard touchdown pass to Michael Hoomanawanui on his first series.