Chadwick Tromp had his first major league hit and RBI for the Giants.
Shin-Soo Choo hit an opposite-field home run for Texas on the game's first pitch.
Flores, the veteran utility infielder who signed with San Francisco in the offseason, made his first start of the season at first base in place of Brandon Belt, who has a lingering Achilles injury.
After a strikeout and a deep flyout in his first two at-bats, Flores hit a 2-2 pitch from Minor into the left field stands to put the Giants ahead 4-2 in the fifth. It was the first home run allowed by a Rangers starter this season and came following consecutive one-out singles by Tromp and Mauricio Dubon.
"I was surprised," Flores said. "I didn't think I got it but with the ball carrying today, it was a good day just to put the barrel on the ball and good launch angle."
Flores also walked and scored as part of San Francisco's three-run seventh.
"Wilmer came into this season all of us knowing that he was such a threat against left-handed pitching, so we kind of envisioned this moment way back in the offseason," Giants manager Gabe Kapler said.
"The whole dugout (has) a ton of confidence in his ability to produce in the big moments. That goes back to our experience watching him as a New York Met when he was kind of the king of clutch," he said.
Texas scored an unearned run off Giants starter Logan Webb in the third but didn't get another hit until the ninth.
Conner Menez (1-0), the second of six Giants pitchers, retired four batters to win.
Minor (0-2) allowed six runs and nine hits in 5 2/3 innings.
Webb gave up four hits and walked four while allowing a pair of runs, one unearned.
The Giants have yet to have a starter make it through five innings after eight games. It's the longest streak to start a season in Major League Baseball history, according to STATS.
They made up for it with one of their best games offensively so far. Eight players had at least one hit and San Francisco put a runner on base in every inning but one.
"We don't have that big bat that's going to hit homers all the time, so we have to keep the line moving, having good at-bats," Flores said. "The rest will take care of itself."
Choo has 24 career leadoff home runs with the Rangers, second in franchise history to Ian Kinsler's 29. Choo was also hit by a pitch for the 151st time in his career, most among active players. . San Francisco's Hunter Pence struck out twice and grounded out twice. Pence is 0 for 21 this season. "Hunter is swinging the bat better," Kapler said. "He's making hard contact. We have no concerns in case that question comes up."
Giants: Belt was rested following Thursday's 10-inning loss to the Padres. . Shortstop Brandon Crawford was also held out of the starting lineup.
Jordan Lyles (0-0, 0.00) makes his first start of the year for Texas on Saturday, four days after the right-hander pitched two scoreless innings of relief. The Giants didn't announce Saturday's starter.
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