Bantams skipper David Wetherall fired home his first goal of the season, but was later sent off as the Robins came from behind to lead 2-1 only for City winger Jermaine Johnson to snatch an equaliser.
City had only bagged three goals in the their last nine games so Wetherall's 15th minute finish was the perfect boost for Colin Todd's men, but Robins keeper Shane Higgs will be cursing his luck.
The keeper superbly pushed out a miscued clearance by Town defender Michael Townsend only for Wetherall to slide in the loose ball from six yards out.
The visitors set out their stall with five men across midfield but they produced the first chance of the game when Nigeria striker Kayode Odejayi headed a Gavin Caines cross wide in the first minute.
After a scrappy opening City finally got the breakthrough after striker Dean Windass was upended on the touchline and Marc Bridge-Wilkinson whipped over the free-kick from the left.
Townsend's mis-hit clearance was brilliantly kept out by Higgs, but Wetherall was perfectly place to fire in the rebound.
The Robins posed few problems for City keeper Donovan Ricketts and when they did get the ball in the net just before the half hour the effort was ruled out.
A long clearance from Brian Wilson gave Odejayi the chance to take on full-back Ben Parker and although midfielder John Melligan slotted home his cross, the linesman ruled that the ball had gone over the deadball line.
The game was turned on its head ten minutes after the break when Wetherall was caught out by a long ball and hauled down hard-running striker Damian Spencer as he surged into the City box.
The City captain was given his marching orders for a second bookable offence and Robins skipper John Finnigan fired home the spot-kick despite Ricketts getting a hand to it.
Three minutes later Cheltenham took full advantage of the extra man when Caines crossed from the right and Odejayi kept his cool to control the ball and place a right-foot shot beyond Ricketts from just inside the box.
Todd made a substitution soon after and it paid dividends after 64 minutes when speedy winger Johnson, who had moved up front, latched on to Windass' header and fired a low left-foot shot beyond the stranded Higgs.
Town could still have claimed the win had Spencer connected with another superb Caines cross after 68 minutes, but the frontman's day ended in frustration as he was shown a straight red card two minutes from time for a heavy challenge on Bridge-Wilkinson.