Elliot Johnson and Evan Longoria added solo blasts to support Price who allowed only one run from six hits and struck out four over eight solid innings.
The Rays, third in the American League East, have won 11 of their past 15 games and five in a row as they attempt to keep touch with the second-place Yankees, who are 7.5 games ahead.
“This was big for us,” Price said. “We’d won four games in a row coming into tonight, and this is a big six-game stretch for us over this next week. It was a big win for us, a good thing for me, and it felt good.”
Sabathia, attempting to win his 17th game and tie Detroit’s Justin Verlander for the most victories, gave up all five runs on 10 hits and struck out five in eight innings, without issuing a walk.
In other AL action, it was:
‧ Red Sox 6, Mariners 4
‧ Angels 5, Blue Jays 1
‧ Rangers 9, Athletics 1
‧ Indians 3, Twins 2
‧ Tigers 5, Orioles 4
‧ Royals 5, White Sox 1