A night after the Giants opened with a 7-1 victory for their seventh straight Series win, Gregor Blanco led off the game with a home run against hard-throwing rookie Yordano Ventura. Brandon Belt tied the score 2-all with an RBI double in the fourth.
Butler's single off Jean Machi drove in his second run of the night and put the Royals ahead 3-2. Perez lined a two-run double to the left-centre wall for a three-run lead, and Infante homered into the left-field bullpen off Hunter Strickland.
Game 3 is Friday night in San Francisco.
Alcides Escobar's RBI double in the bottom of the first off Jake Peavy and Butler's run-scoring single in the second put the Royals ahead 2-1 for their first lead of the Series.
After Infante's homer, Strickland started screaming and got into a confrontation with Perez as he crossed the plate. The dugouts emptied, but no punches were thrown and Hunter was replaced by Jeremy Affeldt.
Ventura allowed two runs and eight hits in 5 1-3 innings and didn't get a decision for the third straight start in the post-season. Kelvin Herrera, one of Kansas City's 100 mph-throwing relievers, escaped a two-on, one-out jam in the sixth and was in line for the win.
Peavy settled down after Escobar's hit, retiring 10 in a row on 28 pitches before Lorenzo Cain's soft single to centre leading off the sixth. He walked Eric Hosmer, and Machi came in and left a fastball up to Butler, who lined it into left for the go-ahead run.
San Francisco tied a World Series record by using five pitchers in the sixth.
After the ceremonial first pitch from retired Royals star George Brett, Blanco drove Ventura's eighth pitch, a 98 mph fastball, into the Kansas City bullpen for his first home run since Sept. 22. It was the 10th home run by the opening batter of a Series game, the first since Boston's Johnny Damon in 2004.
Escobar reached on an infield hit leading off the bottom half, a hard one-hopper that popped out of the glove of shortstop Brandon Crawford, who tried for a backhand stop.
Escobar was caught stealing second by catcher Buster Posey, but Cain doubled with two outs, Hosmer walked and Butler bounced a single past the outstretched glove of a diving Crawford, ending Kansas City's 0-for-17 slide with runners in scoring position dating to Game 2 of the AL Championship Series against Baltimore.
Butler is a .429 hitter (15 for 35) against Peavy.
Making his first start since Oct. 11, Ventura showed the heat that made him the starting pitcher with the highest average velocity in the major leagues this year. He reached 100 mph on his first pitch to Posey in the first.
Infante pulled a double with one out in the second and scored with two outs for a 2-1 lead when Peavy left a first-pitch fastball over the plate and Escobar sliced an opposite-field double inside the right-field line.
Pablo Sandoval doubled leading off the fourth, a drive that bounced off the glove of Cain with his back to the plate near the centre-field wall. Sandoval, who reached base for his 25th consecutive post-season game, scored when Belt hooked a one-out changeup into right field for another double.
San Francisco put two on with one out in the sixth, and the Royals brought in Herrera, usually their seventh-inning man. He retired Belt on a flyout to left and then, throwing at up to 101 mph, got Michael Morse to ground to shortstop for a forceout.
San Francisco, which opened at home en route to titles in 2010 and 2012, was trying to become the first team to win the first two Series games on the road since the 1999 New York Yankees on the way to their sweep of Atlanta. Forty-two of 53 teams to take 2-0 leads went on to win the title, including nine straight since the 1996 Braves lost to the Yankees in six games.
After a day off, the Series shifts Friday to bayside AT&T Park in San Francisco.
NOTES: Baseball Commissioner Bud Selig held a pregame news conference to honour Pete Frates, the former Boston College baseball captain who is afflicted with Amyotrophic Lateral Sclerosis, also known as Lou Gehrig's disease. Frates inspired the ice bucket challenge last summer, and Selig presented an inscribed silver ice bucket to his father, John; mother, Nancy; brother, Andrew, and sister, Jennifer. Frates, 29, was diagnosed 2 1/2 years ago. He is paralyzed and was not able to attend. ... Commissioner elect Rob Manfred presented a pair of new awards for relief pitchers, named after Mariano Rivera and Trevor Hoffman. Kansas City's Greg Holland received the AL honour and Atlanta's Craig Kimbrel was given the NL award.