Smith volleyed home from the edge of the box in the 41st minute from an Andrew Barrowman pass after a mistake by Ian Sharps.
Tranmere sent on Delroy Facey as an extra striker immediately after half-time and put the visitors under severe pressure.
It was no real surprise when they drew level in the 63rd minute. Walsall keeper Andy Oakes could not hold a powerful shot by Facey and Chris Greenacre was left with an easy chance to notch his 15th goal of the campaign.
Walsall refused to lie down and regained the lead in the 73rd minute. Smith this time headed home from a deep cross by Kevin James.
Oakes in the Walsall goal made a terrific first-half save to keep out a Mike Jackson header.
He was also at his best in the second period when turning aside a goalbound shot by Steve O'Leary in the 84th minute.
Walsall were pinned back in defence for the closing stages, but Tranmere could not find a way through.
Oakes did well to block out Calvin Zola and then deep in injury time a Gareth Roberts free-kick from the edge of the box hit the defensive wall.