Play-off chasing Tranmere Rovers won it in the end despite playing over half an hour with ten men, but the result was tough on Danny Wilson's Swindon Town outfit.
Swindon, trying to clear the relegation zone, certainly gave as good as they received but luck was not on their side.
Billy Paynter produced the first goal attempt for the Robins after 13 minutes but it was deflected for a corner by Ben Chorley.
At the other end Petr Brezovan saved comfortably from a 20-yarder by Ian Moore.
The visitors enjoyed a good spell midway through the half but Simon Cox fired wide after good approach work and then had two efforts blocked when he should have done better.
There was no better fortune for Paynter on 32 minutes when he found the sidenetting.
Tranmere struggled to make an impact, but Steve Jennings almost found a way through on 32 minutes only to lose control at a vital stage. As play swung to the other end John Achterberg saved well from Patrick Kanyuka.
Bas Savage was forced off with a leg injury approaching the interval with Terry Gornell joining the home attack. Moments later Moore headed wide from an Andy Taylor centre.
Lilian Nalis replaced Kanyuka for Swindon at the start of the second period.
Tranmere took the lead thanks to a good finish by Antony Kay after he neatly controlled a difficult high ball on the edge of the box as the visiting defence hesitated.
But Rovers were down to ten men on 59 minutes with Goodison dismissed for bringing down Cox just outside the box as he headed goalwards.
Anthony McNamee took over from Kevin Amankwaah for Swindon just after the hour.
Paynter hit a post with an excellent over head shot on 68 minutes, as the ball bounced straight into the arms of a relieved home keeper.
Then Jerel Ifil flashed a header inches wide on 79 minutes.