The 6-foot-7 junior, who also had eight rebounds, had 21 in the first half as the Buckeyes (3-0) built at 10-point lead and cruised through the second half.
Aaron Craft added 18 points for the Buckeyes, who beat Rhode Island on Saturday.
C.J. Wilcox led Washington (2-2) with 18 points and Abdul Gaddy had 15. The Huskies earned the right to play Ohio State with an overtime win Saturday night over Seton Hall.
This is the same tournament that Kentucky won last season in an early test for that young team, which won the national title.
Ohio State led by double digits much of the way and by as many as 17 in the second half. Washington made one run, cutting the lead to 57-50 on a layup by Gaddy midway through the second half, before the Buckeyes stretched it back out.
Thomas scored 11 of his team's first 13 points, showing off his versatility by hitting a 3-pointer, two jumpers, a layup and a hook shot. He hit his first nine shots.
This was his 14th game with 20 or more points at Ohio State. He also scored 31 last season against Loyola (Maryland).
The 6-foot-7 junior was 3 of 7 from 3-point range, and came into the game having made seven of his 15 3-point shots. He had 25 points and 10 rebounds in the Buckeyes' win Saturday over Rhode Island.
Washington stayed in the game in the first half by shooting 52 percent from the floor, led by Scott Suggs who had eight of his 11 at intermission. But the Huskies were outrebounded 34-28 and had 13 turnovers.
These were Ohio State's first games away from home, and first on a neutral court.
The Buckeyes had been scheduled to play on Nov. 9 in the Carrier Classic on the USS Yorktown in South Carolina, but that game had to be cancelled because of condensation on the court.
So the Buckeyes had played just once, a 22-point home win in The Opening game of this tournament over Albany before beating Rhode Island by 11 on Saturday.
The Huskies lost by a point to that same Albany team. Washington led by as many as 18 against Seton Hall on Saturday, but were forced to overtime before winning.
Washington's last win against a top-10 team came in the 2010 NCAA tournament, when the Huskies beat No. 8 New Mexico. Ohio State improved to 4-8 all-time against Washington, a team it hadn't played since 1972.
The Huskies came into the weekend 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.
The game was played at a half-empty Mohegan Sun arena, which is on the grounds of a resort casino and home to the WNBA's Connecticut Sun.
Washington will be back in Connecticut next month, taking on No. 23 UConn in Hartford on Dec. 29.
No. 4 Ohio St. 77, Washington 66
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