Nouha Dicko, who enjoyed a loan spell in the West Midlands last season, reintroduced himself to the Wolves fanbase in style by bagging a first-half brace in his second debut for the club after Sam Baldock had initially levelled matters from the penalty spot.
Bakary Sako wrapped up the points for Kenny Jackett's men with 15 minutes remaining as Wanderers remain within touching distance of the Bees in their hunt for an automatic promotion place back to the Championship.
Dicko struck his first of the afternoon early in the encounter, as the Frenchman fired past City goalkeeper Elliot Parish to give his team the lead inside 10 minutes.
Baldock, who hit a brace in the 2-2 draw with MK Dons last time out, stepped up and kept his cool from 12 yards to restore parity for the visitors.
Steve Cotterill's charges looked to have earned a half-time draw, only for the 21-year-old to pounce again and fire past Parish shortly before the interval.
Sako sealed the victory on 76 minutes by smashing past Parish from 20 yards out to end City's five-match unbeaten streak and solidify his club's clutch on third place, two points behind Leyton Orient.