Yankees 5, Giants 1: Alex Rodriguez broke open a tie game and set a major-league record with his 24th career grand slam in the seventh inning as host New York kept alive its slim playoff hopes.

Alfonso Soriano also homered for the Yankees, who trail Cleveland by three games for the second American League wild-card spot with eight contests remaining but also need to overtake three other teams. CC Sabathia (14-13) recorded one of his finest outings of the season, allowing one run on seven hits over seven-plus frames.

Tim Lincecum (10-14) yielded one run through six innings but departed with two outs in the seventh after loading the bases. Rookie Juan Perez followed up his first career three-hit performance on Thursday with a 2-for-4 effort and drove in the Giants’ only run with one of his two doubles.

After Soriano led off the second with a solo shot and Perez evened it in the third, the Yankees broke through in the seventh after stranding a runner in three of the previous four innings. Eduardo Nunez opened the frame with a single and Brendan Ryan was hit by a pitch before Ichiro Suzuki drew a walk that brought an end to Lincecum’s night.

George Kontos came on in relief and Rodriguez promptly ended a 1-for-25 slump by driving a 2-1 fastball into the seats in right-center field, breaking Yankee legend Lou Gehrig’s all-time grand slam mark. David Robertson tossed a scoreless eighth and Mariano Rivera worked a perfect ninth to close it out.

GAME NOTEBOOK: Rodriguez’s 14th career grand slam as a Yankee moved him past Joe DiMaggio for sole possession of second place in franchise history behind Gehrig. … Lincecum fanned six to become the seventh pitcher to record 1,500 strikeouts with the Giants and first since Gaylord Perry in 1971. … Rodriguez’s 654th career homer put him within six of Willie Mays for fourth place on the all-time list.