The big blast came in the third inning, when Nick Swisher launched a bases-loaded rocket to right field, the grand slam putting an end to a 2-0 Texas lead, sending the Yankees to a series-opening win.
Swisher also singled home Derek Jeter with the Yankees' final run in the seventh, giving him five RBI on the night. Swisher has 15 homers and 63 RBI this season.
The win kept New York five games ahead of the charging Rays, winners of seven straight, while the Rangers extended their lead over idle Oakland to six games in the West.
The series continues Tuesday night in the Bronx with Scott Feldman on the mound for Texas, facing the Yankees' Freddy Garcia.
Improving upon their major league-best road record with a 14-2 slaughter of the Giants, the Nationals continued their road trip with a series-opening, 21-hit barrage, knocking out NL ERA leader, Ryan Vogelsong, with nine hits and eight runs in just 2 2/3 innings.
Five different Nationals had three or more hits, led by shortstop Danny Espinosa, who went 4-for-6, socked his 12th homer of the season, scored three times and drove in three runs. Roger Bernadina also slapped out four hits - a double and three singles - and drove in three.
The Nationals extended their lead in the NL East to 5 1/2 games over the Braves; San Francisco's loss, coupled with the Dodgers' 5-4 win over Pittsburgh, left the Giants and Dodgers deadlocked atop the West division at 63-53.