The 25-year-old's introduction to union had been hotly anticipated after he made the switch from rugby league last month.
Burgess, whose last match was South Sydney Rabbitohs' NRL Grand Final victory in October, has only recently returned to training after sustaining a fractured cheekbone in that game.
But he made a typically action-packed bow for Bath after coming on with 18 minutes remaining at the Recreation Ground.
Having been deployed in the back line, Burgess immediately broke two tackles before being brought down, and five minutes later he was involved again with another powerful run from centre.
A debut try eluded him, but he showed no signs of any problems with his injury and told BT Sport that he had enjoyed his first taste of union.
"It was good, I enjoyed it," Burgess said after the match. "I've been doing a lot of practice, so it was nice to get out on the field.
"I just wanted to try and enjoy it, I did that and we got the win. The whole squad's been great, I have a lot to learn but I'm really enjoying it.
"I was a bit nervous on the bench, but now it's time to focus and knuckle down."
Bath led 13-3 at half-time thanks in the main to tries from Matt Banahan and Kyle Eastmond, and the Quins' hopes were dealt a huge blow when they briefly went down to just 12 men due to three players being sin-binned.
Ross Batty and Leroy Houston also crossed for Bath, who move above Northampton Saints and Exeter Chiefs at the top of the Premiership table.