Hector Noesi matched Bumgarner on this particular evening. The White Sox right-hander and potential fourth or fifth starter yielded one run on two hits over three innings, striking out three and walking one.
Ramirez added a sac fly in the sixth inning, giving him seven RBIs on the spring.
White Sox closer David Robertson made his second Cactus League appearance, giving up two runs on three hits, one walk and one hit batsman in two-thirds of an inning. Erik Johnson saved further trouble on this night by striking out Angel Pagan looking with the bases loaded in the fourth.
Travis Ishikawa, who was briefly a White Sox farmhand in 2013, scored three runs and hit a two-run homer off Johnson.
The White Sox dropped a 7-3 split-squad game to Texas in Surprise earlier on Thursday, but Frank Montas was the story of that contest for the South Siders. Montas, who was acquired as part of the Jake Peavy-Avisail Garcia three-team deal with Boston and Detroit at the 2013 Trade Deadline, touched 98 mph with his fastball. He allowed one run and struck out one in two innings.
"He looked good. The ball came out, he's got some good stuff," said White Sox manager Robin Ventura of Montas. "He can reach back. He can add on, which is nice.
"It's smooth and easy with some movement. But when he wants to he can reach back and get up there around 100, which is always nice to have in your bag."
Up next for Giants: Peavy, who has allowed seven hits in three innings of work spanning his previous two Cactus League starts, will try to even out the imbalance Friday when he starts against the Texas Rangers in Scottsdale on Friday. Left-handers Ty Blach and Javier Lopez also are scheduled to pitch.
Scott Merkin is a reporter for MLB.com. Read his blog, Merk's Works, and follow him on Twitter @scottmerkin. This story was not subject to the approval of Major League Baseball or its clubs.