Abdul Gaddy had 16 points and Suggs had 15 to help the Huskies to an 84-73 win in the Hall of Fame Tip-Off tournament in Connecticut.
Led by Suggs, the Huskies outscored the Pirates 13-2 in the extra period.
"I felt pretty good the whole game," Suggs said. "This morning was my first practice (since the injury)."
The Huskies (2-1), coming off a one-point upset to Albany on Tuesday, led by as many as 17 in the first half against the Pirates.
But Seton Hall (2-1) responded, scoring 23 of the first 30 points after intermission and going up by as many as six in the second half. Fuquon Edwin had 20 of his 27 points after halftime to lead Seton Hall.
Suggs opened overtime with a 3-pointer, and freshman Andrew Andrews hit another on Washington's next possession, giving the Huskies a 77-71 lead.
The Huskies got two offensive rebounds on their next possession and ran the clock down to 2:04 before Gaddy hit a pair of foul shots.
Edwin hit a layup to cut the lead back to six, before another 3-pointer by Suggs pushed the lead to nine and put the game away.
"Given a second chance, I was confident we could do it," Suggs said. "We were fortunate to come out on top."
For much of the game, it didn't appear this one would be close.
Washington used a 17-0 run to take an early 17-5 lead and led 45-28 on a jumper by C.J. Wilcox. The Huskies shot over 61 percent from the floor in the first half were up 49-33 at the break.
But Seton Hall responded in the second, scoring 23 of the first 30 points.
A steal by Aaron Geramipoor and a 3-point shot by Kyle Smith tied the game at 56 with 9:24 left. A layup by Patrik Auda gave the Pirates their first lead since early in the first half at 60-58, and a 3-pointer by Edwin made it 63-60.
"I thought Fuquon in the second half really turned it up defensively and really caused havoc defensively, which really got his offense going," Seton Hall coach Kevin Willard said. "When he is creating havoc for us, we're really good."
But Washington tied it at 66 on Desmond Simmons' basket with just over 3 minutes left, and the neither team could put the other away.
The game was tied at 71 after Aziz N'Diaye hit one of two free throws after being fouled on a put-back with 57 seconds left. Edwin then missed a layup, giving Washington the ball with just under 18 seconds left.
But Simmons dragged a pivot foot at the top of the key with 7.4 seconds left and the Pirates got the ball back.
Patrik Auda's 3-pointer just before the buzzer missed everything, sending the game into overtime.
Simmons and N'Diaye each had 14 points for Washington. Wilcox added 11.
Suggs was hurt when he fell and hit the back of his head on the knee of an Albany player early in Washington's loss on Tuesday. But he started this one and scored his team's first points on a jump shot that stopped a 5-0 Seton Hall run to open the game.
Coach Lorenzo Romer said his Huskies are a much better team when he is on the court.
"At the end, he played like a true senior, hit big shots for us and played good defense," Roamer said. "He makes a difference."
Washington came into the game having lost six games in a row to nonconference opponents on the road. The Huskies were 0-5 on the road against nonleague teams last season.
Washington will be back in Connecticut next month, taking on No. 23 UConn in Hartford on Dec. 29.
Several thousand Seton Hall fans made the trip up Interstate 95 from New Jersey. They are expected back Sunday to watch the Pirates play Rhode Island, a campus that is just 40 miles from the Mohegan Sun arena.
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