It was the 10th career shutout for Taylor but his first of the season.
Taylor and the Heat defence shut down the highly-touted Oklahoma City offence, laden with Edmonton Oiler star Taylor Hall, Ryan Nugent-Hopkins and Jordan Eberle.
Ben Street and Ben Walter each had a goal and an assist for Abbotsford (7-1-2). Dustin Sylvester and Krys Kolanos also scored, while T.J. Brodie had a two-assist game.
Barons goaltender Yann Danis made 32 shots in the losing effort.
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The NHL talent on the visiting Barons (5-5-1) was not lost on the 7,046 fans at the Abbotsford Entertainment and Sports Centre. Both Friday and Saturday's rematch are sold out, the first time a Heat game has sold out versus anyone other than the affiliate of the nearby Vancouver Canucks.
The Heat opened the scoring with 70 seconds remaining in the first period on a power play. Street's shot was kicked right to Sylvester at the side of the net and he slid the rebound past Danis for his fourth of the season.
Abbotsford doubled their lead on a second-period power play at 8:34. Street took a cross-ice pass from Sven Baertschi and snapped a shot past Danis that may have deflected off an Oklahoma City stick.
The Barons were stymied by both their own errors and some bad luck. Early in the second frame they had the goaltender well out of position but twice threw the puck through the crease and wide of the net. Then on a power play Nugent-Hopkins one-timed a feed from Hall but the puck was right on Taylor, making for an easy stop for the Abbotsford goaltender.
The bad luck culminated with an own-goal by Martin Marincin. From behind his own net the Oklahoma defenceman tried to feed a pass up ice but it deflected off fellow defenceman Alex Plante at 17:09. Walter was credited with the goal, his third of the season.
Kolanos scored on a two-man advantage midway through the third. He took a great cross-crease pass from Walter and picked the corner from in close to increase the Abbotsford lead to 4-0.
Abbotsford finished 3 for 9 on the power play while their league-best penalty killing unit was successful on all five chances.