Garcia (4-3) gave up just two runs and four hits in seven innings.
Price (7-2) allowed three runs over seven innings. His only other loss this season also came against the White Sox.
Alex Rios hit a two-run homer for Chicago.
White Sox bench coach Joey Cora filled in for manager Ozzie Guillen, who was attending the high school graduation of his son.
In Minneapolis, Kevin Slowey allowed only one run pitching into the seventh allowing Minnesota to scratch out a tight win over Texas.
After failing to get through the sixth inning in eight of his first nine starts this season, Slowey (6-3) struck out five over 6 2-3 innings. Jon Rauch earned his 11th save.
Joe Mauer was 1 for 3 for the only Twins RBI.
Rangers starter Colby Lewis (4-3) gave up five hits over six innings.
In Detroit, Miguel Cabrera hit three home runs in a game for the first time in his career, but it wasn't enough for Detroit to beat Oakland.
Landon Powell homered and drove in two runs for the A's.
Oakland reliever Brad Ziegler (2-2) gave up one hit in the eighth inning to take the win, while closer Andrew Bailey shut down Detroit after giving up a leadoff homer to Cabrera.
Tigers reliever Ryan Perry (1-4) gave up two runs to take the loss.
In Boston, Yuniesky Betancourt hit a grand slam to cap a seven-run fourth inning as Kansas City trounced Boston.
David DeJesus had four hits and the Royals combined for 20 off six Boston pitchers.
Kansas City had five straight singles to open the fourth, and with two out Betancourt lofted a knuckleball from Tim Wakefield (1-3) into the seats above the Green Monster in left for the second grand slam of his career.
The Royals pummeled Wakefield for 12 hits and nine runs in just 3 2-3 innings.
Mitch Maier had three hits for the Royals, including his first home run of the season.
Royals starter Kyle Davies (4-3) worked five shaky innings for the win.
In New York, Phil Hughes returned to form with seven strong innings to guide New York past Cleveland.
Hughes struck out the first five batters he faced and allowed two runs.
Robinson Cano hit a grand slam, had three hits and scored three times batting cleanup in place of Alex Rodriguez, who got the day off.
For Cleveland, Russell Branyan hit a homer and Jhonny Peralta had an RBI double.
Indians starter Fausto Carmona (4-3) gave up four runs in six innings.
In Toronto, Aaron Hill and Vernon Wells hit solo home runs to help Toronto down Baltimore.
Hill hit an RBI single in the first and added his solo homer to left in the sixth. Five of Hill's last eight hits have been home runs.
Blue Jays pitcher Shaun Marcum (5-1) allowed threw six innings, walking only two and striking out seven, to win his fourth straight start.
Toronto is 4-0 against Baltimore this season.
Orioles starter Kevin Millwood (0-5) allowed five runs, four earned, in six innings and is winless in 11 starts this season.
In Anaheim, Cliff Lee struck out 10 in eight innings to guide Seattle past Los Angeles.
Lee (3-2) allowed two earned with two walks in his 200th big league start.
Milton Bradley drove in three runs for the Mariners.
Angels starter Scott Kazmir (3-5) gave up six runs — five earned — in 5 1-3 innings. He has a 6.91 ERA over his past five starts.
In his first game at Angels Stadium since leaving in the off-season, Chone Figgins was 1 for 3 with two walks and two runs scored for Seattle.
