The Moroccan somehow scooped the ball over the crossbar from almost on the goalline as Wolves enjoyed much the better of the second half after Villa were on top in the opening period.
Villa, needing a win to rekindle their top-four hopes after losing to bottom club Sheffield United in midweek, twice hit the woodwork in a largely forgettable first half.
The draw left Villa in ninth place on 40 points from 26 games with Wolves in 12th spot on 35 points.
Although both sides were guilty of missing golden chances, it was a tepid derby and point each was about fair.
Villa were again without chief creator Jack Grealish but were the more dangerous side early on.
"I couldn't do much more about the shot that hit the bar. I hit that sweet and started to celebrate," Watkins said.
Then came Saiss's miss. When a cross came over Wolves defender Conor Coady should really have scored but his header hit the post and rebounded across the area where Saiss sent the ball almost vertically up and over the bar.
Coady had another great chance when the ball came to him in a crowded penalty area but from point-blank range his shot was saved by Martinez.
"We were more like ourselves in the second half and a bit more on the front foot so disappointed," Coady said.
"I didn't see Romain Saiss, I just saw it go over the bar, I just thought try and keep it down but I should score. Massively disappointed."
Watkins almost won it for Villa at the death before Konsa lashed wildly at the rebound to sum up a disjointed game.
"I keep saying there is a lot of inconsistency around the Premier League at the moment with the exception of Manchester City," Villa manager Dean Smith said. "There is tiredness and fatigue."