The Giants are now only two points behind leaders Nottingham.
It was a successful night for the Giants and the first in action since players left en masse for a team now owned by the Odyssey Trust.
Colin Shields became the team's leading point scorer after an assist on the second goal.
Giants took the initiative early by killing off an opening minute penalty and then taking advantage of their own first powerplay opportunity by going ahead at 3.04 with a strike by Kevin Saurette.
Despite outshooting Stars 18 to 8 in that opening period that was to be the only counting shot.
Period two was goalless but again the Giants were having more of the play and fired 14 shots on Nic Riopel as against only 7 on Garrett Zemlak and it was into the third session before the hosts made a more even fight of proceedings.
However, there was just no way past Zemlak as he ended up making 23 saves for his fourth shutout as a Giant, having only joined the team in January.
The one goal lead was finally advanced by a strike from Jeff Mason as the defenceman ended a 20 game scoring drought by firing in at 54.24 to ice both points for Doug Christiansen's men.