Dozier's slam, the first for the Twins this season, helped them move within 1 1/2 games of the Rays and Royals for the second American League Wild Card spot.
• Grand slams mean 40% off pizza
"That was probably the most excited I've been, and not because of the grand slam, but just the fact the crowd was into it, taking the lead against a good team and where we're at," Dozier said. "It's that time of year where it kind of picks up. So that was exciting."
Dozier has been heating up recently, hitting five homers over his last eight games to raise his season total to 21. He finished strong last year, hitting 13 homers in August and 10 in September.
"I think Garza started him out with a fastball his previous two at-bats," manager Paul Molitor said. "I was just hoping he wouldn't try to pull a pitch that was un-pullable. Thankfully, he let it get deep, and the couple home runs he's hit to right field this week haven't been cheap. One went off the façade a few days ago, and this one cleared the bleachers. So, it's a great approach with a guy on third with less than two outs."
Dozier said he thought Garza would try to pitch him away, and he took advantage, jumping on a fastball that caught too much of the plate.
"I knew he wasn't challenging me inside, so I got on the plate," Dozier said. "If he threw me a fastball, I thought it would be down and away, but he left it up."
Rhett Bollinger has covered the Twins for MLB.com since 2011. Follow him on Twitter @RhettBollinger and Facebook. This story was not subject to the approval of Major League Baseball or its clubs.