David Johnson was close to his 22nd goal of the season on the six-minute mark when he headed David Prutton’s cross narrowly wide.
Walsall failed to capitalise on Junior’s run when he squared to Darren Wrack who shot wide.
Tompson gave the home side the lead they deserved after a long spell of possession ended with another whipped in cross by Prutton, and his half volley six yards out left keeper James Walker with no chance.
Midway through the first half the Saddlers had their first shot on target, this coming courtesy of a Zigor Aranalde who never threatened Darren Ward's goal and was comfortably saved.
In the opening minute of the second period Walsall's Gareth Ainsworth worked his way clear on the byline, but his shot hit the side netting when a squared ball across the crowed box may have proved more fruitful.
Walsall were a different team after the break and in the 63rd minute their persistence paid off with an equaliser.
Darren Bazeley crossed to Ainsworth, who hit a low shot that nestled in the back of the home goal.
Forest picked up their game and came close to a second, but Johnson’s wayward shot ensured the points were shared.