Injury-hit Teversal were beaten 4-3 at Eccleshill United as their miserable run continued.
The Tevie Boys, who had 11 players missing, started brightly and were rewarded with a goal on four minutes when Robinson was hacked down in the box.
Matt Langley stepped up and drilled the spot-kick against the post, but debutant Ollie Roome reacted the quickest to fire the rebound past Stead to get the visitors of to the perfect start.
Eccleshill really should have levelled when a defensive lapse allowed Flaherty with the time and space to roll in an inch perfect ball to Edwards who missed with the goal open.
Teversal made their host rue those missed chance when Toby Birch beat Stead with to a glancing header at the near post to beat Stead to make it 2-0 after 24 minutes.
Eccleshill came out in the second half with lots of possession as the visitors looked happy to sit back and defend their lead.
But they soon learned that it was the wrong way to go as the home side pulled one back on 53 minutes when Josh Rosenstraugh got the better of a challenge with Langley before slotting past Brooks.
Teversal failed to heed the warning and four minutes later the scores were level when Edwards broke and pulled the ball back to Rosenstraugh to clinically finish from 12 yards.
Eccleshill totally turned the game on its head on 61 minutes when Flaherty had time to place a weak effort that beat Brooks to make it 3-2.
Credit must be given to the Tevie Boys who reverted back to the high tempo that gave them their half-time lead and they became a threat to the host again.
But Teversal were left facing an uphill task when Craig Newton was shown a second yellow card.
The sending off though didn’t deter from the Tevie Boys efforts who pushed the home-side on the back foot until the 88th minute when a long punt up the park sent Edwards clear.
Langley raced back to force the striker to fire a low drive that Brooks superbly saved, but the ball ran straight to Ismael Mills who thundered his effort to the back of the net to make it 4-2.
Mark Robinson marked an excellent performance with a stunning goal from 20 yards out as he fired into the top corner with Stead having no chance to make it 4-3.
It took some desperate blocks to deny Roome and Dawson on the dying minutes to prevent Teversal leaving Bradford with something from a game.