Buster Posey added a solo homer in the sixth as San Francisco earned its third consecutive win. Posey, who won the NL MVP award in 2012, went 1 for 3 and is batting .103 (4 for 39) over his last 13 games.
Indians right-hander Zach McAllister was in complete control before he got into trouble in the fifth. He needed just seven pitches to get through the third and seven more to retire the side in the fourth.
McAllister (3-1) retired 12 in a row before Michael Morse led off the fifth with a single to center. Morse advanced to third on Brandon Crawford's one-out single and scored on Gregor Blanco's pinch-hit single.
Angel Pagan had a sacrifice fly before Pence's two-out hit gave the Giants a 4-3 lead.
McAllister left after Brandon Belt struck out to end the inning. He allowed five hits, struck out six and walked one after winning his previous three starts.
Giants starter Tim Lincecum lasted just 4 2-3 innings, but managed to lower his ERA to 5.96. He was charged with three runs, two earned, and nine hits.
Lincecum has pitched just 25 2-3 innings in five starts in his first season since he signed a $35 million, two-year contract over the winter.
Romo got three outs for his sixth save in six chances as San Francisco's bullpen lowered its MLB-best home ERA to 0.45 in 11 games.
Cleveland scored in the first, third and fifth to build a 3-0 lead. Kipnis singled in Bourn in the first and drove in Swisher with a grounder in the third. Swisher doubled home Bourn in the fifth.
Saturday marked the 257th straight regular-season sellout at AT&T Park, matching the National League record set by the Philadelphia Phillies from July 7, 2009 to Aug. 5, 2012. Up next on the MLB sellout streak list is the Indians, who sold out Jacobs Field 455 times from June 12, 1995 to April 2, 2001.
NOTES: The Giants have now started off interleague play with two consecutive wins against the Indians after going 6-14 in 2013, the second-worst mark in MLB. ... McCallister registered his first career hit in the second inning with a single to right field. ... Giants Hall of Famer Willie Mays helped escort 3-year-old Cody Harrington to the mound to throw out the ceremonial first pitch. ... Right-handers Ryan Vogelsong (0-1, 7.71 ERA) of San Francisco and Danny Salazar (0-3, 7.85 ERA) of Cleveland enter Sunday's series finale in search of their first win of the year.