The two teams were tied 6-6 at halftime.
The Orange will finish its ACC schedule with a trip to North Carolina to take on the Tar Heels this weekend.
Virginia Tech scored four straight goals in the last seven and a half minutes of the game to bring the Orange within one.
Syracuse dominated draw controls, winning 20-7.
Syracuse limited Notre Dame to only one goal in the second half.
Brendan Curry took 12 shots but only scored one goal.
The Orange won 16-of-22 draw controls against the Crimson.
Syracuse closed the game on an 8-1 run
The Orange scored six goals in the final quarter