Swindon skipper Sean O'Hanlon scored a dramatic late equaliser to rescue a point after striker Dean Windass looked to have secured a much-needed win for Bradford.
Windass missed two great chances in a one-sided first half, but he made amends when his half-volley 11 minutes from time finally broke the deadlock.
But City's season has been plagued by too many draws and they failed to hold out again as O'Hanlon headed home the leveller in the last minute of normal time.
City's defence, which had hardly been troubled all match, was caught flat-footed by Aaron Brown's right-wing corner and O'Hanlon got to the near post first to head home the equaliser from six yards.
It was cruel on the Bantams who had bossed the game from the start, but they paid a heavy price for failing to make the most of their early dominance.
Just when they looked like drawing a blank for the second home game in a row, Windass reacted quickest to Marc Bridge-Wilkinson's flick header and this time the marksman made no mistake as he guided his eight-yard left footer beyond keeper Rhys Evans.
A minute earlier Evans had produced a sensational save to tip over a rasping drive from Danny Cadmarteri and the keeper's excellent display got its reward when O'Hanlon secured a share of the spoils.
City's season has been blighted by a miserable run of three wins in 16 games and they were again guilty of wasting several good openings.
After just two minutes a smart counter attack was ruined by Cadamarteri's poor control and midway through the half Windass fluffed a great chance when Evans saved his close-range header.
Two minutes before the break Evans was called into action again as he smothered a Windass strike following an incisive three-man move.
There was little change after the break as the Bantams continued to make the running, but they still could not find the killer touch in front of goal until Windass fired home his 16th goal of the season.
But two wins on the bounce have revived Swindon's hopes of avoiding the drop and although they struggled to create much in front of goal, their battling spirit was epitomised by O'Hanlon who hurled himself at Brown's corner to snatch their seventh point from three games.