Stony Brook is 1-6 in its last seven one-goal games, including a 1-3 record this season.
Siena outscored Stony Brook, 4-0, in the fourth quarter after trailing by as many as four, 9-4.
After leading 5-4 at halftime, Stony Brook exploded for six goals, two on man-up, in the third.
Watson's third of the game gave the Seawolves the five-goal lead. Siena scored two straight to cut it to 9-7, but Bonanno's 10th goal of the season made it 10-7.
Sophomore Matt Bellando (Miami, Fla.) made it 11-7 with 25 seconds left in the third quarter, but Colin Clive answered with three seconds left in the quarter to cap a 10-goal period.
"I thought we completely stopped playing and got tight," head coach Jim Nagle said. "Our conference season starts on March 31, and we'd better get things right."
Neufeld scored two goals in the final period, including the game winner with 7:02 left. Stony Brook had two shots in the final two minutes but both were saved by Tom Morr, who finished with 15 saves.
Stony Brook travels to face Bryant on Saturday, March 24 at 1:00 p.m.