On Friday, Gillies made 44 saves and was named the second star in the Heat's 5-3 victory in San Diego.
Stockton jumped out to a 3-0 lead in the first period but Gillies was forced to hold his team in for the remainder of the game, with the Gulls peppering him with shots all night.
"There were spurts in the game that I felt busy," Gillies recalled. "[San Diego's] power play moves the puck really well, so even if they're not getting a lot of quality shots they move it around the perimeter really well. That makes you feel like you're exerting a lot of energy, but other than that I thought they had a couple good chances, but we did a good job of keeping them to the outside.
"We played a good, insulated game and I'm happy to come out with the win."
Gillies followed up Friday's strong play with his best game of the season, denying the Gulls on 48 of the 49 shots they sent his way on Saturday.
Once again, the Heat grabbed a 3-0 lead and relied on Gillies to hold off a Gulls squad who put 11 shots on net in the opening period, 13 in the second stanza and 25 in the final frame.
"On the second night of a back-to-back as a goalie, as long as your legs aren't heavy you're able to get into the rhythm a lot faster," Gillies noted. "We came out and we jumped on them early, which is what we've been doing lately, but we knew they were going to have a push back.
"When that comes it's my job to stand up to them. I had a lot of help [on Saturday] and we were able to close it out thankfully."
Gillies' best stop on Saturday came in the second period when Gulls winger Nick Sorensen came in on a breakaway. He attempted to beat Gillies high but the netminder was able to get a glove on the shot.