Alexei Ramirez hit his second homer of the game with two outs in the 10th inning to lift the White Sox to a 6-5 win over the Oakland Athletics on Tuesday night.Ramirez also hit a three-run shot in the second inning and scored a run after drawing a walk in the sixth.Chris Sale (2-0) picked up the win with two shutout innings.Daric Barton had four hits and scored a run, and Kevin Kouzmanoff hit a two-run homer for Oakland. Hideki Matsui, who entered the game hitting .182, had three hits, including a double, and drove in two runs.Bobby Cramer (0-1) took the loss for Oakland.Adam Dunn made his return to the lineup after missing the last six games because of an emergency appendectomy April 6. He went 1 for 4 and drew a walk in five plate appearances.The A’s went ahead in the second inning when Mark Ellis lined a double to the wall in left-center, scoring Ryan Sweeney from first.Oakland righty Trevor Cahill was making his first start since agreeing to a new five-year contract on Monday. If Cahill was still celebrating his new pact, the White Sox cut the party short, putting him on the rocks early.Cahill escaped the first inning without a run scoring despite allowing a single, a walk and throwing two wild pitches. He wasn’t as fortunate in the second.Ramirez hammered his second homer of the season on a hanging breaking pitch to put the White Sox up 3-1. They added another run in the inning on Paul Konerko’s grounder, but Cahill settled down after that, retiring six batters in a row.He ran into more trouble in the fifth. Dunn hit a leadoff single before a two-out error by shortstop Andy LaRoche put two runners on with two outs.Cahill’s pitch count was up to 97 and the lefty-hitting Pierzynski was coming up, so Oakland manger Bob Geren summoned lefty Craig Breslow from the bullpen. Breslow got Pierzynski on a flyout to left to end the inning.Cahill threw 4 2/3 innings, allowing six hits, four runs, walking three and striking out three.Oakland manufactured a run in the third, capitalizing on Barton’s leadoff double when Matsui brought him home on a groundout.Jackson was coming off a dominant performance in which he struck out a career-high 13 over eight innings in a win over Tampa Bay on April 7.Jackson couldn’t make it out of the fifth on Tuesday, costing him a chance at his third win in three starts even though he departed with the lead.Matsui drove in the Athletics’ third run, singling with two outs in the fifth to score Coco Crisp and cut the deficit to 4-3.Kurt Suzuki reached on a error on a grounder bobbled by Ramirez. That came on Jackson’s 100th pitch of the night, which turned out to be his last.Ozzie Guillen brought in reliever Will Ohman, who got Sweeney on a fielder’s choice to escape the threat with the lead intact.Jackson went 4 2/3 innings and allowed seven hits and three runs while walking two and striking out four.The Athletics took advantage of a Sox wobbling bullpen in the sixth. Ellis started with a single off Tony Pena and scored when Kouzmanoff launched a homer into left field, putting Oakland ahead by a run.The Athletics then loaded the bases against Pena, but the righty escaped the jam by striking out Suzuki.The White Sox evened the score in the sixth, turning Ramirez’s leadoff walk into a run on Juan Pierre’s solid single to left off Breslow.

NOTES—SS Cliff Pennington was unavailable for the Athletics because of what Geren called “a little infection of his sweat gland.” Geren said his availability is day-to-day. … Geren said Athletics reliever Michael Wuertz (hamstring) will likely throw a simulated game on Thursday, followed by a start in a minor-league rehab game on Saturday. … White Sox OF Lastings Milledge cleared waivers on Tuesday and accepted an assignment to the club’s Triple-A affiliate in Charlotte. … LaRoche’s throwing error in the fifth snapped Oakland’s streak of six-plus games without an error. The Athletics committed an Oakland-record nine errors in their first four games.