Simon Cox gave Swindon the lead from close range on 15 minutes to make it 1-0.
On 27 minutes the score was level again at 1-1 after a Grant McCann free kick from 20 yards out found the back of the net.
Smith was then kept busy for the rest of the first half, but pulled off a number of good saves to keep Swindon level going into the half time break.
Woolfood made it 2-1 to Scunthorpe on 50 minutes.
It wasn't long before Swindon were back in the game with Cox beating the offside trap and was able to lob the 'keeper to make it 2-2 after 52 minutes.
Pearce made it 3-2 on 58 minutes after a free kick on the edge of the box was headed in from close range.
Scunthorpe's keeper Murphy shouted abuse at some of the Swindon fans behind the goal, which made him very unpopular.
Then on 79 minutes Paynter was fouled in the box. Simon Cox took the penalty and sent Murphy the wrong way to make it 3-3, and complete Cox's second hatrick of the season.
Both sides pushed for a 4th goal, and both come close, but the game fnished 3-3 which was a fair result after a good game from both sides.