The visitors had gone in front in the first half through Sam Mantom and looked capable of holding on to the lead in an exciting game which flowed from end to end, but two goals from Andy Williams turned the contest on its head.
Williams' first goal after 63 minutes was a bit of a fluke. Jonathan Franks' shot from the edge of the box and bounced off the back of Williams to loop over goalkeeper David Grof.
Williams claimed his 10th goal in as many matches to win the game after 84 minutes, hooking a left-wing corner goalwards as Walsall substitute Anton Peterlin helped it into the net as he attempted to defend.
"We took the lead against the run of play in the first half, but in the second half we had lots of chances. It was too much end-to-end for my liking but we should have killed the game off," said Smith.
"Yeovil's goals were heartbreaking but they seem to be having a lot of luck at the moment. They were lucky when they won 2-1 at Oldham last week, but that's the way it goes."
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