Highly-rated Wales international Hennessey made his crucial intervention in the 85th minute after Neill Collins had pulled down Craig Beattie.
Zoltan Gera stepped forward to take the spot-kick but Hennessey flew to his right to beat the ball away.
The point was no more than Wolves deserved after they spiked Albion's big guns.
Albion's free-scoring attack drew a blank for only the second time this season against a Wolves side who have the joint best defensive record in the Championship.
Wolves have not won at The Hawthorns since 1996 and they could have ended that long wait for a win had Seyi Olofinjana not wasted golden chances in each half.
But the draw did at least stretch their impressive run to just one defeat in 11 games.
Albion should really have taken a lead into half-time as they dominated in terms of possession for the opening half hour.
After Ishmael Miller had fired off-target early on, Filipe Teixeira missed a golden chance when he lifted the ball over the bar from just 12 yards after a left-wing cross from Chris Brunt.
Miller then shot weakly at Hennessey in the 32nd minute, before Wolves finally worked their way into the game in the final ten minutes of the half.
Olofinjana should really have given Wolves a 35th minute lead when Michael Kightly whipped in a right-wing cross.
Olofinjana was unmarked just six yards from goal but steered his header the wrong side of the post.
Stephen Ward then saw his 20-yard drive deflected just wide before Darron Gibson was inches away from breaking the deadlock with a long-range drive on the stroke of half-time.
Albion thought they had taken the lead through Teixeira 11 minutes into the second half, but Hennessey tipped his curling 20-yard drive on to the post.
Hennessey then dived bravely at the feet of Beattie before Olofinjana squandered his second excellent opportunity.
He was picked out by a near-post cross from Kevin Foley but stabbed his shot into the sidenetting.
It would have been a crucial miss but for the penalty heroics of Hennessey.