The 33-year-old former England international, who has endured an injury-hit season, grabbed his first goal in more than a year four minutes after coming on as a substitute.
Ravel Morrison also scored twice to take his tally to four in three matches as Rangers collected only their second win in eight attempts.
"It was very pleasing to score three, to get a win and a clean sheet, and for Bobby Zamora to score," said assistant manager Kevin Bond.
"It's great for Bobby, I thought he did really well when he came on. You could see the goal made a big difference for his confidence and it gave the whole place a lift.
"So it's great to have him back around us. I don't see why he can't play a big part. At his best he's been a top-class player.
"Those days may be fewer and farther between nowadays and he's had his injury problems, but he looked fully fit and raring to go today."
West Ham loanee Morrison opened the scoring with another classy finish midway through the first half. The 21-year-old tip-toed along the 18-yard line, delaying his shot with a couple of neat feints before unleashing an unstoppable drive in off the post.
The second goal arrived in the 70th minute when Zamora nodded in an inviting cross from Junior Hoilett. And Morrison grabbed his second to kill Yeovil off in the last minute when he tucked in Niko Kranjcar's pass.
"Ravel has got that quality that can make a difference in games, he can do something special when something special is required," added Bond.
"It's his fourth goal for us and he's done really, really well."
The only downside for Rangers was yet more injury problems with Jermaine Jenas and Armand Traore limping off with hamstring strains and goalkeeper Rob Green suffering suspected cracked ribs.
The scoreline was tough on Yeovil, though, after they had an early Luke Ayling goal disallowed and saw Tom Lawrence hit a post at 1-0 down.
"I think it was harsh, we had a great first 20-odd minutes and it would have been nice to be one up," said manager Gary Johnson.
"Then they got their goal and we hit the woodwork which was a great strike and they just aren't going in for us at the moment.
"So we're a bit disappointed to lose by three goals but I don't think we've lost anything with the teams around us down the bottom, results went the way we wanted them to and we are still fighting."