Thy paid for the lack of production.
Jake Petricka started the ninth for the White Sox after Chris Sale sailed through eight shutout innings. Pablo Sandoval, Mike Morse and pinch-hitter Travis Ishikawa each singled to load the bases for Joe Panik.
Panik hit a ball up the middle that Beckham somehow gloved and started a double play, with Sandoval scoring.
"If the ball gets by we're talking a different game," Giants starter Ryan Vogelsong said. "Gordon made a great play and saved the game for them right there."
Adam Dunn hit a two-run home run off Vogelsong in the first.
"I wasn't even trying to throw a strike," Vogelsong said. "My two-seamer was running all over the place in the bullpen but for some reason that one stayed on the plate. He's a big, strong man and he put a good swing on it."
Zach Putnam (4-2) pitched 1 1-3 innings for the win.
Sale struck out 12 and walked two over eight solid innings in his best start of the season. It's the 16th time in 77 career starts that Sale has fanned 10 or more — second-most in franchise history — and a team-record ninth time with 12 or more.
Vogelsong struck out five and walked two in six innings. He allowed only one hit following Dunn's home run — a leadoff triple by Conor Gillaspie in the second — then retired the next seven.
It wasn't enough to keep San Francisco from falling a season-high six games behind the Dodgers in the AL West. The Giants led the division by 9 1/2 games on June 8 but have gone just 20-36 since.
"Hunter is as good a baserunner as we have," Giants' manager Bruce Bochy said. "He got a late jump and the shortstop read it. You hope it doesn't play a factor but it ends up being a one-run loss for us."
Pence thought he could play it safe before taking off.
"That's a pretty good play by their shortstop, and gutsy," Pence said.
RHP Matt Cain underwent season-ending surgery to remove bone chips in his pitching elbow. Recovery is expected to take three months of rehabilitation. ... C Hector Sanchez (concussion) has resumed his rehab with Triple-A Fresno.
White Sox: LHP Jose Quintana (6-8), who has one loss over his previous 10 starts, makes his first career appearance against San Francisco in the final half of this brief two-game series.
Giants: RHP Jake Peavey, winless in three starts with the Giants, allowed one run over six innings against Chicago on April 15 when he was still with Boston.