Harang, who signed a minor-league free agent contract on Feb. 15 after pitching for Seattle and the New York Mets in 2013, won his second spring start in a row as he makes a bid for a spot in the Indians' rotation.
The Indians scored a run in the first inning on a bases-loaded walk issued by Tim Hudson. After the Giants tied it at 1 in the second, Cleveland scored two more in the third. Swisher led off with his first homer of the spring and the second run scored on a double-play ground ball.
Indians: Bench coach Brad Mills said the 6-foot-7 Harang, who has also pitched for Oakland, Cincinnati, San Diego and the Los Angeles Dodgers during a 12-year career, brings a strong veteran presence to the mound.
Mills, who managed the Indians while manager Terry Francona managed the other split-squad team against the Chicago Cubs, said the 35-year-old Harang "still has got pretty good stuff. His fastball can sneak up on you and he can keep you in the game.
"He throws strikes and always seems to be around the plate."
He said Harang really made only one mistake, in the second inning, when a pitch ran out over the plate and Juan Perez hit it for a triple. Perez scored on a single by Brandon Crawford.
Giants: Hudson is trying to stretch himself out, and he threw 100 pitches Sunday in his fourth start of the spring.
He said it wasn't one of his worst outings, command-wise.
"I actually felt pretty good out there. I was just missing on a few pitches.
"I need to get the pitch count up. I need to get my work in. I have two or three more starts before the real thing."
He covered first base on a few grounders hit to first baseman Brandon Belt, a test for the right ankle that was broken during a similar play last July that ended his season with the Atlanta Braves.
"It's not graceful by any means, but I'll take it," he said of covering the bag, adding that he might get some residual soreness from time to time but that it is nothing to worry about.
Indians: Center fielder Michael Bourn, the team's leadoff hitter on Sunday, left after his second at-bat in the second inning due to mild tightness in his left hamstring. He will be re-evaluated on Monday.
Giants: Left fielder Michael Morse continues to be sidelined with tightness in his calf. Second baseman Marco Scutaro has yet to appear in a game because of back soreness, but has now taken batting practice and grounders for four consecutive days.
SWISHER SWINGS IT
Swisher, the veteran switch-hitting first baseman-outfielder-DH, collected a pair of hits, including his first spring homer, as well as a walk. His average climbed to .200.
"It's nice to see him start to get back into it. It looks like he is seeing the ball real well," Mills said.
HALL OF FAMERS RULE
Four of the Giants' five living Hall of Famers addressed the team before Sunday's game - Orlando Cepeda, Willie Mays, Willie McCovey and Gaylord Perry.
GIANTS HIT THE ROAD
The Giants will play three road games (Angels, Indians, Padres) and have an off day before returning to Scottsdale Stadium to face the A's on Friday night.