Nigel Adkins' men had the chance to extend their advantage over second-place West Ham to eight points ahead of the Hammers' late kick-off against Derby, but instead they suffered their first defeat in 16 games.
Albert Adomah's second-half strike put the Robins in front before Nicky Maynard sealed City's second home win of the season in the 84th minute.
Cardiff opened up a two-point gap over Middlesbrough in third after they beat Nottingham Forest 1-0 thanks to a 70th-minute header by Joe Mason.
Tony Mowbray's side claimed a point at Peterborough with a 1-1 draw after Posh's Paul Taylor equalised in the 81st minute following Matthew Bates' earlier goal for Boro.
Leeds are four points adrift of Boro in fifth after they went down to a surprise 2-1 defeat against Barnsley in the Yorkshire derby at Elland Road.
Ricardo Vaz Te blasted into the roof of the net from Jim O'Brien's centre to put the Tykes in front at Elland Road before they extended their lead on the stroke of half-time when Leeds goalkeeper Alex McCarthy fumbled Jacob Butterfield's half volley to leave Craig Davies with a simple finish.
Ross McCormack pulled one back from Leeds from a free-kick but it was not enough as Leeds' poor home form continued.
Blackpool moved into the play-offs despite conceding a late equaliser in the 2-2 draw with Birmingham at Bloomfield Road.
Marlon King gave Birmingham the lead shortly before the half hour to notch his fifth goal of the season before the Seasiders found an instant response through full-back Stephen Crainey's prodded finish. Neal Eardley looked to have sealed the win for Blackpool in the second-half before Nikola Zigic salvaged a point for the Blues in the 87th minute.
Source: PA
Source: PA