Alain Goulet fired home a slap shot with 55 seconds left in regulation to give the Bears a point, but four separate shooters could not beat Greenville goalie Connor Knapp in the shootout.
"We battled them right to the end," Solar Bears head coach Drake Berehowsky said. "I thought we had more chances than them — we had a couple of breakaways we missed on, a couple of open nets we missed on. But I'm proud of the way the guys played."
Olivier Fortier seized the moment in his return from the AHL's Hamilton Bulldogs, scoring two goals and an assist. In 32 games with Hamilton, the winger was primarily used as a penalty killer, only notching two total points.
"I'm really happy to be back. I played quite a bit tonight; I'm not used to it," Fortier said. "I like it here way better because it's always nice to score goals and have points."
"I got frustrated a lot of the time [in Hamilton]. I didn't really get the chances I used to get in previous years up there."
Mark Nemec, a defenseman from the University of Maine, scored his first professional goal in the second period. His college teammate, Kyle Beattie, had a career-high three assists.
Nemec was only added to the roster several hours before game time, flying into Orlando early Thursday morning.
"Coming here was kind of hectic, but I was pretty comfortable on the ice," Nemec said. "I went from shoveling my car out [of a foot of snow] yesterday to sunshine and palm trees."
Nemec paired with Derick Martin, the only Solar Bear to play all 67 games this season.
"He's a steady defenseman who can play a lot of minutes," Berehowsky said of Nemec. "He's hungry to get to the next level, and he wants to learn."
Marc-Olivier Vallerand and Jordie Johnston scored two goals each for the Road Warriors. Johnston and Brendan Connolly provided the markers in the shootout.
The Solar Bears finished the season series with three wins in eight meetings against Greenville.
The Solar Bears will get back to action Sunday when they host the Cincinnati Cyclones for the first time at 3 p.m.
Orlando will look to avenge a 4-0 defeat to their former IHL rival.