Rochdale have now gone three matches without a point or a goal but they made Swindon work hard for their win and there was little between the sides.
Rochdale had been more than a match for Swindon for most of the first half with Chris Dagnall forcing a good save from Czech newcomer Petr Brezovan.
But then a minute before the break Swindon striker Christian Roberts centred from the left and Goodall, under no pressure, headed past his startled goalkeeper for a calamitous own-goal.
Adam Rundle forced another good save from Brezovan before Goodall was involved in another potentially damaging incident.
Goodall lunged at Ricky Shakes on the edge of the area when there was no apparent danger to concede a spot-kick.
But Goodall was redeemed when Matthew Gilks dived to his left to parry the penalty to safety.
Roberts could have had a hat-trick after missing his penalty as he wasted two other good chances.
After 54 minutes Paul Evans played him clear of the defence only for Gilks to come off his line to make the save.
Then after 68 minutes Roberts got away from the Rochdale defence again only to drive his shot straight at the goalkeeper.
There was another penalty incident after 72 minutes and another fine piece of goalkeeping from the busy Gilks.
Ernie Cooksey handled a centre from Evans and it was Evans who stepped up to replace Roberts as the spot-kick taker.
This time Gilks dived to his right and Evans' penalty struck his foot before rebounding wide.
After surviving such a battering, Rochdale almost forced an equaliser with eight minutes remaining but Brezovan clung on to a long-range shot from Lee Crooks.