The Raiders (22-12, 6-7) took a 1-0 lead in the bottom of the first after Missouri starter Abel Newton walked leadoff hitter Jon Slack, who later scored after a stolen base, passed ball and wild pitch.
Jake Brown extended his current hit streak to nine games in the bottom of the second when he picked up an RBI single to give Tech a 2-0 lead.
In the bottom of the fourth inning, senior shortstop Gera Alvarez extended his current hitting streak to 15 games with a double down the left field line.
His double helped spark a three-run burst for Tech, which tallied three hits in the inning, including an RBI single by Slack.
Missouri (10-14, 2-8) got on the board in the top of the sixth inning when the Tigers scored twice on RBI singles by Jody Roughton and Mick Weiss.
Sophomore Brent Fossum put the game out of reach in the bottom of the eighth with a two-run pinch-hit home run.
Missouri added two more runs in the top of the ninth before senior reliever Steve Rowe struck out the final two batters to end the game.
Chris Phillips (4-2) picked up the win for Tech while, Abel Newton (3-2) suffered the loss for Missouri. Rowed added his fourth save this season after pitching the final 2 1/3 innings.
Weather permitting, Tech and Missouri will play again today at 2 p.m. in the second of a three-game set at Dan Law Field.