It was the redshirt senior's second career double-double and first this season.
Derrick Gordon added 13 points for UMass (8-7, 1-1 Atlantic 10), which made 27 of 52 (52 percent) field goals.
A pair of free throws by Jordan Price pulled La Salle (8-7, 0-2) within one, 61-60, with five minutes to play, but the Explorers went 2 of 9 from the field down the stretch.
Layups by Esho and Gordon gave UMass a five-point lead before Steve Zack made the second of two free throws to make it 65-61.
Esho and Trey Davis each made both ends of one-and-one opportunities in the final 1:45 to hold off La Salle.