Alvarez's homer was his sixth this season. It was set up by a leadoff single to center by Jon Slack, Willie Durazo's walk and Nick Blankenship's 21st hit-by-pitch this season.
Missouri (10-15, 2-9) tied the score in the top of the third inning with four runs. The Tigers got RBI doubles from Ryan Rallo and Jody Roughton and RBI singles from Cody Ehlers and Lee Laskowski.
Mick Weiss gave Missouri a 5-4 lead in the top of the sixth with a solo home run over the right field wall.
Tech retook the lead in the bottom of the seventh, scoring two runs on three hits. Slack led off the inning with a single to center and Scooter Jordan also singled. Durazo slapped a base hit to right field in the next at-bat, which scored Slack.
Tech got its second run of the inning on a double play groundout by Blankenship that pushed across Jordan.
Missouri tied the score in the top of the eighth on an RBI single by Mick Weiss to knot the score at 6-6.
Slack put Tech back in the lead with an RBI single up the middle and Durazo delivered a bases loaded two RBI single for a 9-6 lead.
Blankenship added his 13th home run of the season when he deposited an inside slider over left field to give Tech a 12-6 lead.
Steve Rowe (5-1) got the victory in relief, allowing only two hits. Matt Hobbs (1-3) suffered the loss for Missouri, surrendering five earned runs in just 1 1/3 innings of work.