With out in the seventh, Chicago first baseman Jose Abreu fielded Joe Panik's broken-bat grounder to easily throw out Blanco. Giants manager Bruce Bochy challenged the play, and umpires ruled Flowers' left leg was illegally blocking the plate before the ball arrived.
White Sox manager Robin Ventura argued the call and was immediately ejected, setting off an epic protest in which he repeatedly kicked dirt on the plate.
San Francisco snapped a five-game losing streak and Jake Peavy (1-3) won for the first time since April 25 with Boston. Peavy had lost 12 consecutive decisions, the longest skid of his career.
Jose Quintana (6-9) took the loss.
Adam Dunn hit his 19th homer of the season into McCovey Cove in the fourth for Chicago's only run. It was one of just four hits Peavy allowed in seven innings.
Peavy even changed his uniform number from 43 to 22, which he wore for his high school in Mobile, Alabama. He wore 44 with the San Diego Padres, White Sox and Boston Red Sox.
Perhaps the new look changed his luck.
Blanco was tagged out well before he slid into the plate in the seventh. But under Major League Baseball's expanded instant-replay system that began this season, San Francisco took advantage of a rule that prohibits catchers from blocking the plate so runners don't barrel into them.
The review lasted 4 minutes and 55 seconds.
Umpires also allowed Adam Duvall to advance from first to third. But even after being ejected, Ventura came back out to challenge that decision. The play was reviewed again, and umpires told Duvall to go back to second.
Quintana was relieved by Ronald Belisario after walking pinch-hitter Joaquin Arias to load the bases with two outs. Angel Pagan followed with a two-run single, and Hunter Pence and Buster Posey each hit RBI singles.
Center fielder Jordan Danks and Dunn got tangled up in right-center going for Pablo Sandoval's fly. The ball dropped, and two more runs scored to give the Giants a 7-1 lead.
Quintana was charged with four runs and four hits in 6 2-3 innings. Belisario was tagged for three runs, one earned, and three hits without recording an out.
White Sox: Pitching coach Don Cooper, who did not make the road trip because of a recurrence of vertigo-like symptoms, is expected to rejoin the team in Chicago on Friday.
Giants: Backup C Hector Sanchez (concussion) was scheduled to start behind the plate Wednesday with Triple-A Fresno for the first time during his rehab assignment, while 1B Brandon Belt (concussion) and 2B Marco Scutaro (lower back) remain out indefinitely.
White Sox: After a day off Thursday, RHP Hector Noesi (6-8, 4.67 ERA) starts the opener of a three-game home series against Toronto on Friday.
Giants: The team has a day off Thursday before LHP Madison Bumgarner (13-9, 3.22) takes the mound in the opener of a three-game series against Philadelphia on Friday