Parens was 22-for-24 on face-offs and scored a crunching goal with just 0.5 seconds left in the third quarter to put the Camels up 11-7.
Connecticut College had a 37-29 shot advantage and helped its own cause by not taking a penalty.
Sean Smith had three goals and one assist to lead the Camels, who trailed 2-1 after a quarter and 6-5 at halftime. Jackson Kleintz added two goals and one assist, Tucker Mscisz had one goal and two assists, and Maximilian King scored twice.
Austin Sayre had a game-high four goals to lead the Mules. Colton Michel added two goals and one assist, Lane Kadish had two goals, and Tucker Dietrick dished two assists.
Colby took some momentum into halftime when Sayre scored his third goal of the first half with just 17 seconds to play.
However, the Camels came out strong and scored six goals in 15 minutes. King scored from Jordan Foster to tie the game at 6-6 just 1:39 into the third quarter. PJ Kelleher gave Connecticut College its first lead at 7-6 with 11:16 to go.
Colby settled down over the next five minutes and tied the game at 7-7 on a blast by first-year Lane Kadish with 5:37 left in the third quarter.
The Camels scored four goals in the final 4:40 of the quarter to take control. Smith and Mscisz made it 9-7 and then the Camels devastated the Mules with two goals in the final 6.5 seconds. Smith scored with 6.5 seconds remaining off a nice feed from Kelleher. Parens then won the face-off, quickly scooped up the ground ball, sprinted toward the goal, and ripped a shot in with 0.5 seconds to play.
Colby did manage to score two goals and kept Connecticut College off the scoreboard in the fourth quarter. Sayre scored his fourth of the game with 9:19 to play and Michel tucked in a shot at the right post with 5:20 remaining. The Mules had a few chances to cut the margin to one goal, but could not score.
Anthony Drouin led the Camels with two caused turnovers and two ground balls. Alex Calabro and Jake Bank also had two ground balls.
Sean Dougherty paced the Mules with three caused turnovers and one ground ball.
Jameson Hill played the first half and the fourth quarter in goal, making five saves for the Camels. Hunter Rosenthall stopped one shot in the third quarter. C.J. Layton finished with nine saves for Colby.