The Fighting Tigers took the lead for keeps at 65-64 when Jack Jeffres scored inside with 1:30 to play.
Tyrone Mitchell made it a three-point spread on a driving layup with 33 seconds left and Jeffres capped the scoring on two free throws with 10 seconds remaining.
Woods, a freshman, also had five blocks. Mitchell and Jeffres scored 17 and 15 points, respectively, for Cobleskill, which will host Gallaudet at 2 p.m. Saturday.
Thristan Lundy had 14 points for Penn State Harrisburg (8-10, 5-3).
Delhi 67, Schenectady 55
Stefan Bock scored a team-high 16 points to lead SUNY Delhi to a road win Sunday.
Sean Scott scored 10 points and had 11 rebounds for the Broncos (18-2), who will host Columbia Greene on Tuesday.
Delhi 84, North Country 82, 2OT
Quayshaun Mitchell made two three-point baskets in the finals seconds of double overtime on Saturday to lead visiting Delhi to victory.
North Country led, 82-78, with less than 30 seconds left in the second overtime. Mitchell scored from the top of the arc with 22 second left to make it 82-81.
North Country turned the ball over on its next possession, when the Saints lost the ball out of bounds against the Broncos’ press.
Delhi ran a play for Mitchell on the inbound play, finding him along the baseline. His three-point shot with 12 seconds left gave the Broncos the lead. The Saints then missed a three-point shot at the buzzer.
“It was a big-time shot, and he just buried it,” Delhi coach Rob Schoener said of Mitchell’s go-ahead three.
North Country rallied from five points down in the last minute of the first overtime to tie the score.
“Our whole team just has a will to win,” Schoener said. “I was telling their coaches after the game, we had no business losing the game in the first overtime, and we had no business winning it in the second overtime, but our kids found a way.”