The Leopards (8-13, 3-3 Patriot League) led 40-34 at halftime and started the second half on a 16-4 run to extend their lead, 56-38, with 16:14 left to play.
A jumper from Rob Delaney gave Lafayette its biggest lead, 83-57, with 1:36 left on the clock.
Ella Ellis scored a game-high 28 points and pulled down 10 rebounds for the Black Knights (10-11, 2-4). Jeremy Hence added 12 points and Julian Simmons, Army's leading scorer at 15.5 points per game, scored just three points on 1-of-9 shooting.
Petkovich finished 6 of 8 from 3-point range for Lafayette. Tony Johnson added 13 points and Jim Mower 11 for the Leopards, who shot 51.7 percent from the floor (30 of 58) and outrebounded Army 40-26.