Alexander (6-2) had his bid for a perfect game end on a throwing error by shortstop Keaton Jones to lead off the seventh. Andrew Knizer followed with a single to right to end Alexander's shot at a no-hitter. The sophomore lefty struck out six and had 15 flyouts in his first complete game of the season.
The Horned Frogs (46-12) and Wolfpack (36-22) play again Monday, with the winner advancing to the Super Regionals.
Derek Odell's two-run single gave TCU a 2-0 lead in the second, and Dane Steinhagen's two-run triple in the third made it 5-0.
Wolfpack starter Ryan Williamson (4-4) gave up seven hits and five runs in 2 2/3 innings.