The visitors took a 37th-minute lead at Ashton Gate when Jay Dasilva crossed from the left and Tatsuhiro Sakamoto outjumped his marker to net with a downward header.
Coventry's Joel Latibeaudiere was sent off shortly before half-time for denying a clear goalscoring opportunity but deep into first-half stoppage time the Sky Blues doubled their advantage when Haji Wright beat Radek Vitek with a low right-footed drive.
The game became 10-a-side in the 56th minute when Bristol City midfielder Adam Randell was shown a second yellow card for a high challenge on Josh Eccles.
From then on Coventry defended strongly to secure the points, securing a fifth league win in a row.
Millwall climbed to third, strengthening their play-off hopes as second-half goals from substitute Mihailo Ivanovic and Josh Coburn earned their side a 3-1 win at Hull.
Promotion-chasing Ipswich, now fourth in the table, were held 1-1 by relegation-threatened Leicester.
Patson Daka put the Foxes ahead in the 39th minute but Sindre Walle Egeli equalised for the hosts in the second half.
Leicester remain in the drop zone, a point behind West Brom, who scored a late equaliser at Sheffield United.
Derby kept up their push for a play-off spot with a 2-1 victory over relegated Sheffield Wednesday.
Wednesday become only the fifth team in Football League history to go 30 or more consecutive games without a win.
The top two teams are automatically promoted to the Premier League, with the four clubs finishing from third to sixth competing for the remaining place in the top division via the play-offs.
Second-placed Middlesbrough travel to face QPR on Sunday.