With a low drive into the far corner by David Clarkson the home side, with only two wins in their previous 18 games, thought the points were theirs, but seconds later Lloyd Dyer pulled out a similar shot to rescue the Foxes.
He raced over to the travelling fans waving his shirt above his head but the yellow card hardly mattered.
After shading most of the game the point was invaluable for his side as they kept up their challenge for the play-offs.
They had tested Bristol's fragile self belief early on when Dyer from the touchline dropped a tantalising ball into the area. But as it came in Dean Gerken was tempted off his line but Andy King beat him to the ball.
Racing across the goal with a lunging tackle Liam Fontaine rescued his keeper and then from the corner blocked Matty Oakley's fierce drive.
Leicester were on the front foot but somehow couldn't find the shots. Martyn Waghorn, deputising for the injured Matty Fryatt, put plenty of energy into his game but his timing let him down in the first half as he was three times ruled offside.
A greater threat came from Paul Gallagher's long-range free-kicks. The first was spilled by Gerken for a corner, the second veered just outside his right post.
The home side's best chance of a disappointing first half also came from a set-piece after Bruno Berner had been booked for hauling down Danny Haynes, who had got by him down the right.
Lee Johnson produced a nicely weighted ball which Louis Carey racing past defenders lifted over the bar.
Carey though was always a pivotal figure in a rather inconsistent home defence.
This so nearly proved fatal around the hour when no-one moved to shut down Michael Morrison as he launched a long solo run down the right flank. The defender's cross was good, but under pressure Waghorn's shot from around the penalty area was just off target.
Waghorn then worked a smart one-two with Oakley which ended with his captain stabbing an eight-yard shot against the foot of a post.