Walsall took the lead after only 8 minutes after a mistake by Morrison allowed Deeney to score from 10 yards out to make it 1-0.
Walsall had most of the play in the first half, with Swindon rarely looking like scoring.
In the second half Swindon looked a much improved side, and it looked as if it would only be a matter of time before their scored.
Ex Swindon striker Sam Parkin played for Walsall in the second half, and he was given a good welcome from the 735 Swindon fans who had made the journey to the Bescot.
Swindon had one penalty appeal turned down, then a couple of minutes later they were awarded one after Paynter had his shirt pulled in the box. Paynter took the kick, but hit the post.
Then on 79 minutes Swindon were awarded another penalty after a hand ball in the box. Paynter again took the kick and this time scored to make it 1-1.
Overall a good game, with Walsall being the better side in the first half, and Swindon being the better second half side, so a draw was a fair result. This leaves Swindon in 7th place with 13 points.