Poly had a definite shot advantage in the first half, but didn't cash in a goal until the 30th minute when Harrison Hodgkins' 15-yard shot from the right side was deflected by Rebels goalkeeper Brian Heintz backward into the net.
Just six minutes later, Poly (8-5, 2-1) padded its lead on an awkward glancing shot by Jack Porter that rolled to the left post, bounced off it and trickled into the goal before Heintz (six saves) or the Rebels defense could react.
"[They were] unlucky goals," Gautrat said. "First goal, we didn't have the cover near post, second goal we didn't have cover on our outside back. But, honestly, I couldn't be more proud of them. They worked really hard."
Early in the second half, the Panthers took firm control of the match on a 36th-minute goal by Brian Holman, who had room to get a shot off in the middle of the Rebels' penalty box in the 44th minute.
The Rebels began to pick up their attack later in the second half, as Harris and Cole Rademacher each got shots off before Harris took a pass from Jesse Redding and made good on a high-arcing header that Poly's goalkeeper tried to leap to secure, only to see it glance off his mitts and just under the crossbar into the upper right corner.
With time on the Panthers' side, the Rebels' final push included a close-range running shot by Rademacher in a one-on-one situation with a defender, but the shot was smothered.
The two rival teams will meet again at 3:30 p.m. on Feb. 4 at Prep.
"It's all about the process," Gautrat said. "Keep building, keep working hard and not worry so much about the results."