The win means City now have eleven points from seven matches.
Leaders Wolves won 3-1 at Preston. Chris Iwelumo hit a hat-trick before getting sent off in the 76th minute. Mick McCarthy's side also had keeper Wayne Hennessey sent off.
Second placed Birmingham were beaten 1-0 at home by Blackpool, whom, City travel to next Saturday.
Preston are third, QPR are fourth and Bristol City who beat Doncaster 4-1 are fifth and Reading who drew 2-2 at Watford thanks to a John Eustace own goal which never was, lie in sixth place.
Barnsley, are bottom after a 0-0 draw at Southampton with Forest in 23rd place after their 0-0 drawe at home to Charlton.
Plymouth beat Crystal Palace and all the games finished in draws.
Liam Davis scored Northampton in a 3-2 defeat at Huddersfield. Lee Hughes scored for leaders Oldham. Andy Morrell hit his third goal for Bury in a 2-1 win at Barnet.
Locally, Tony Dobson's first league game in charge of Rugby Town brought a 3-2 defeat at Oxford City.
Leamington still have maximum points from six matches in the BGB Southern League Midland Division. Goals from Corbett and a brace from Bellingham saw a 3-2 win at Soham Rangers.
Atherstone Town are in second place with a 2-1 win at Woodford United. Nuneaton Town beat Bury Town 4-1 in front of a crowd of 692 with former City Reserve teamer Mark Noon on the scoresheet. Bedworth also had a good win with a 2-1 victory at Arlseley.
In the FA Vase, Racing Club Warwick beat Rocester 3-1 and Stratford Beat Gedling by the same score.
Former Coventry Sphinx striker Craig Martin scored twice for Coventry Copsewood in a 4-2 defeat at Brocton. Nuneaton Griff won 3-2 at GSA whilst Massey Ferguson beat Knowle 3-0.
Stockingford beat Burntwood 10-1 but Coventry Amateurs lost 2-0 to Coton Green Res and Kenilworth Town were beaten 5-0 at home by Shirley Town.