The A's No. 7 prospect smacked a ninth-inning grand slam in Oakland's 11-7 Cactus League victory over the Texas Rangers in Surprise, Ariz.
Acquired by the A's in the six-player deal that sent Gio Gonzalez to the Washington Nationals in December, Norris helped cap a dramatic comeback with his late heroics.
With the bases loaded and the game tied, 7-7, Norris pulled incoming reliever Derek Hankins' third pitch -- a 1-1 cutter -- down the left-field line to give the A's what proved to be the decisive lead.
"Our second group of guys, those are the guys you take pride in finishing up games," manager Bob Melvin told MLB.com. "They've got tremendous energy, and it's nice to see."
In nine Spring Training appearances, Norris, one of seven backstops in camp with the team, is batting .250 with five RBIs.
Selected by the Nationals in the fourth round of the 2007 Draft, Norris -- the South Atlantic League's Most Outstanding Prospect in 2009 and MiLB.com's Class A Hitter of the Year in '10 -- batted .210 with 46 RBIs and 38 extra-base hits for Double-A Harrisburg last season.
The 23-year-old also was chosen to play in the elite Arizona Fall League. In 21 outings, Norris hit .276 with two homers and 11 RBIs en route to being named an AFL Rising Star and being selected to the All-Prospect team.
On Thursday, Cliff Pennington went 4-for-4 with two doubles, two RBIs, a run and a walk, and leadoff batter Jemile Weeks was 3-for-4 with three runs and two RBIs. Evan Scribner (1-0) tossed two scoreless innings of relief to pick up his first win.
Texas' No 4 prospect Leonys Martin was 1-for-2 off the bench to raise his spring average to .222.