Iain Hume missed two glistening chances for the Foxes in the first half, and Bristol 'keeper Adriano Basso produced a superb injury-time save to deny Steve Howard, as they hung on for a point.
Elsewhere, Stoke City moved up to second after they earned a late point at home to Burnley.
Kyle Lafferty opened the scoring for the away side, but a last minute Liam Lawrence penalty saved Stoke and extended their unbeaten run to 11 games.
Meanwhile Colchester remain bottom of the table after a 2-1 defeat away at Crystal Palace.
Palace opened the scoring with 21 minutes gone when Phil Ifil turned the ball into his own goal from Danny Butterfield's cross.
However, Colchester equalised two minutes later thanks to Kevin Lisbie's solo goal.
Clinton Morrison had a goal disallowed for the home side, before they regained the advantage with a goal from Ben Watson.
Watson drilled past Dean Gerken from a right-wing cross to leave Palace just three points off the play-off positions.
Second bottom Scunthorpe United were beaten by rivals Hull City in the Humber derby to leave them seven points from safety.
Henrik Pederson put City ahead with a header inside the first half-hour, and the lead was doubled ten minutes later when Michael Turner converted Andy Dawson's corner past Iron 'keeper Joe Murphy with a powerful header.
The result means Hull move into sixth place, whilst Scunthorpe stay in the relegation zone.
Sheffield Wednesday earned a much needed three-points as they hosted QPR.
However, it was the away side that took the lead when Damien Delaney finished past Lee Grant after good work from Rowan Vine down the left wing.
Patrick Agyemang then drilled his shot against the post, before Wednesday equalised just before half-time.
Franck Songo'o clipped the ball through for Graham Kavanagh who headed past Lee Camp in the Rangers goal.
The home side then took the lead from the penalty spot after Sean McAllister was brought down by Grant in the area. Deon Burton scored to seal the win.
Paul Sturrock's Plymouth dropped out of the top six after they were beaten by Sheffield United at Home Park.
James Beattie grabbed the only goal of the game after 63 minutes with a header at the far post from David Cotterill's cross.
Southampton slipped two places to fourth from bottom after they were held to a 2-2 draw away at Blackpool.
Goals from Gregory Vignal and Stern John were cancelled out by Keith Southern and Kaspars Gorkss at Bloomfield Road.
In the final two games of the day, Charlton Athletic were beaten 2-1 at home to Preston North End, and Norwich City were beaten away at Coventry City 1-0.