Garza allowed one run over seven innings and division-leading Tampa Bay beat the Seattle Mariners 9-1 on Saturday night.
Matt Joyce and B.J. Upton homered for the Rays, who moved 1½ games ahead of the New York Yankees. Tampa Bay, bidding for its second division title in three years, has a magic number of two (any combination of Rays wins or Boston losses) to clinch a playoff berth.
"We know what we're after," manager Joe Maddon said. "It's fun to watch. The way we're going about business right now, I couldn't be happier."
The Rays hold the tiebreaker if they finish the regular season tied with New York. Tampa Bay has won four straight, while the Yankees have lost four in a row.
Garza (15-9) allowed eight hits, struck out five and walked none. He was 0-2 with a 10.93 ERA in his previous three starts.
"He definitely set the tone," Maddon said. "Stayed in his delivery better. Commanded the strike zone better."
Garza joined David Price (18-6) as the only pitchers in franchise history to have 15 or more wins in a season
"It's a special year," Garza said.
Joyce hit a two-run drive during a four-run first. Upton had a seventh-inning solo shot and added an RBI triple during a three-run eighth.
"I think the best thing is just us winning and our lineup producing," Rays catcher John Jaso said. "Not really like being ahead of other teams and all that stuff. We want to be playing up to our full capabilities going into the postseason."
Franklin Gutierrez singled home a run in the sixth for the Mariners, running his team-best total to 60 RBIs.
Seattle dropped to 23-54 on the road and has lost seven of eight against Tampa Bay in the season series.
Fister allowed four runs and five hits in six innings.
"I thought after the damage was done he did a nice job of keeping it there," Mariners interim manager Daren Brown said.
Garza induced an inning-ending double play from Gutierrez with two on in the first and got Ichiro Suzuki to hit a two-out grounder with a runner on third in the fifth.
Upton's homer and a run-scoring single by Carl Crawford extended Tampa Bay's advantage to 6-1 in the seventh.
Seattle left fielder Mike Carp left in the fifth with a strained right arch. He was hurt while running the bases on a double.
Rays All-Star 3B Evan Longoria (left quadriceps strain) missed his second consecutive game but expects to return in the next three or four days. "It feels a lot better and we'll go from there," Longoria said. ... Seattle closer David Aardsma (left oblique strain) is expected to be sidelined for the next two or three days. RHP Brandon League will serve as the closer while he's out. ... Crawford tied his team record set in 2004 when he scored his 104th run of the season in the first. ... Fister retired 10 in a row after Joyce's homer. ... Tampa Bay 1B Carlos Pena was hitless in four at-bats, dropping his batting average to .198. He does have 27 homers and 81 RBIs in 136 games.