Walsall dominated a lively first half, but Wrexham fought back strongly after the break and Chris Llewellyn levelled. But he also missed two good openings when he might have finished with a hat-trick.
The Saddlers were disappointed to drop two points and they picked up fifth bookings for Ian Roper and Martin Butler which will see both players suspended for the next game at Boston.
Matt Done shot wide from Wrexham's first chance and Kris Taylor's early free kick for the Saddlers was also off target as both sides jostled for position.
Craig Pead had a shot blocked by defender Shaun Pejic and, when Sam put in a dangerous cross, Ryan Valentine nipped in to clear off Mark Wright's toe when a goal seemed certain.
Sam's goal, his fifth of the season, came when Anthony Gerrard flicked on from Wright's corner and found the striker perfectly placed to head in at the near post.
Wrexham raised their game later and Llewellyn should have equalised early in the second half but headed over from five yards.
Lee McEvilly was sent on as a substitute after an hour and tested keeper Clayton Ince with a power drive from 15 yards.
Llewellyn's goal put Walsall under late pressure but Wrexham spurned other chances as Marc Williams produced a weak header and McEvilly shot wide.