Garbowsky had opened the scoring in the contest with 3:49 left in the first period. His initial shot was denied, but the puck ricocheted right back to him in the slot and he buried the rebound chance.
Avalanche prospect Julien Nantel got the primary assist on Garbowsky's first goal. Nantel also had three shots and a plus-2 rating while on one of the Eagles' top forward groups in the game.
Colorado outshot South Carolina 27-15 through the first 40 minutes of play, but the team couldn't build on its lead and was back to square one after Scott Tanski recorded his first tally of the postseason for the Stingrays midway through the second stanza.
Moments before South Carolina took the 2-1 lead in the final minutes of the third period, Boikov left for the team's locker room after getting hit in the head by the puck while sliding on the ice to break up a pass. He did return midway through the first overtime and finished the contest.
"It's part of the game. It was worth it," Boikov said afterward.
Mason Geertsen, another Avalanche prospect, had one shot and two penalty minutes, but his biggest contribution might have come on the penalty kill in extra time.
With South Carolina on the power play early in the second OT and with control of the puck in the offensive zone, the Eagles found themselves in a predicament as two of their players had lost their sticks. As time was ticking away on the man advantage, Geertsen had a key block before Colorado regained possession and cleared the puck out, allowing the squad to regroup and finish the PK.
"I just tried to get as big as I could and pray that it hit me, and it did," Geertsen recalled of the sequence. "We then got it out, which was a good play by [Cam] Maclise to get it out."
South Carolina went scoreless on its seven man advantages.
"I think we are pretty composed on the PK," Geertsen said. "We know what we have to do. It's to be hard and get pucks out. I think that was a big key tonight."
While the Eagles seemed like the better team in regulation, it was the Stingrays that appeared to have more energy during the first overtime session. South Carolina outshot Colorado 10-6 in the period after the Eagles had dominated the statistic through regulation, with a 34-23 edge in shots on goal.
However, the second OT belonged to the Eagles as they only allowed one shot on Hafner, who finished with 31 saves and made several key stops in the final three frames to keep the score tied.
"I thought in the first overtime, we didn't move our feet very well," Nantel said. "We were kind of soft. After that in the second overtime, we were moving our feet, good speed. That is what we have to do next game at the start."
Game 2 of the best-of-seven championship series is Sunday at 7:30 p.m. in Loveland.