Bourret, acquired in the off-season by the parent Phoenix Coyotes, opened the game’s scoring at 12:50 of the first period and eventually broke a 1-1 tie with a power play goal at 19:54 of the middle stanza.
In between, the Wolves received an even-strength goal from Joey Crabb – his first of the season – at 17:47 of the opening period.
The defending Calder Cup champions finished their season-opening trip to Texas at 0-1-1-0. After visiting Quad City on Friday, the Wolves will begin the home portion of their schedule on Saturday against Peoria.
San Antonio goaltender Josh Tordjman earned the victory in Wednesday’s contest by stopping 25 of 26 Chicago shots, and the Rampage’s penalty-killing unit went a perfect 8-for-8 on the evening.