New York ended a three-game losing streak and moved in front by a game over Baltimore in the American League East.
The teams battled to a 4-4 tie through six innings before the Yankees came up with two unearned runs on a defensive miscue.
With the infield playing in, Derek Jeter hit a hot grounder directly to second baseman Elliot Johnson. Suzuki broke for the plate immediately and Johnson fired home. His throw, however, sailed past the glove of catcher Chris Gimenez all the way to the backstop.
Suzuki scored and Pearce never slowed down, easily coming in as well before Gimenez could recover the ball.
Tampa Bay fell to 2 1/2 games behind the Yankees after having a four-game winning streak snapped.