Norcross scored two runs in the sixth inning Tuesday to squeak by Lambert, 3-2, in Game 1 of a three-game series.
Lambert led 2-1 heading into the sixth, but a leadoff walk issued by Courtney Sauer and a pair of singles came back to bite the Longhorns.
Brooke Miller led Lambert at the plate, finishing 3 for 4 and driving in a run. Sauer had a pair of hits and scored a run.
Lambert totaled eight hits but left a pair of runners on base in the third inning and stranded two more in the fifth inning.
Kirsten Cowart got the no-decision for Lambert, pitching four innings while giving up one run on four hits and walking six. Cowart also struck out three batters.
Sauer took the loss after surrendering two runs on four hits across two innings.
Allie Sewell, Anna Jackson and Cowart each finished with one hit.
Lambert (10-16) must win Game 2 tonight to force a third game, which would be 5:30 p.m. Wednesday.