Anthony Jackson added 10 points, six assist and five rebounds for Stony Brook (8-2).
Stony Brook led 55-54 with less than 3 minutes to play but Shane Gibson’s jumper put Sacred Heart (2-7) on top 56-55 with 2:31 left on the clock.
Warney responded with consecutive baskets, a dunk and a layup to put Stony Brook ahead 59-56 with 1:19 remaining.
After Gibson turned over the ball, Dave Coley hit a 3-pointer to extend the Seawolves’ lead to 62-56 with 30 seconds to play.
Three Gibson free throws cut Sacred Heart’s deficit to three, but Anthony Jackson connected on two free throws with one second left to seal the victory.
Gibson led the Pioneers with 22 points.