Carl Cort tapped in the opener from close range after a one-two with Mark Kennedy but the Hatters were on top and Steve Howard wasted a headed chance.
Ahmet Brkovic saw his header superbly saved by keeper Michael Oakes and home frustration grew when boss Mike Newell was sent off at half-time.
Steve Robinson hit the bar with another header and Cort fired wide for Wolves before Nicholls levelled from 12 yards.
Wolves boss Glenn Hoddle:
"It's a good point in the context of the 90 minutes.
"We knew they were going to be tight on us, they work that to their favour.
"I thought our back four stuck to their task well, as did Michael Oakes in goal, we allowed them to put too many balls in our box but we dealt with them."
Luton: Beresford, Edwards, Coyne, Heikkinen (Perrett 87), Davis, Underwood, Nicholls, Robinson, Brkovic, Feeney (Showunmi 70), Howard.
Subs Not Used: Morgan, Holmes, Brill.
Booked: Edwards, Feeney, Nicholls, Davis.
Goals: Nicholls 79.
Wolverhampton: Oakes, Edwards, Lescott, Gyepes, Naylor, Kennedy, Anderton (Olofinjana 60), Seol (Cameron 88), Ricketts, Miller (Clarke 28), Cort.
Subs Not Used: Craddock, Postma.
Booked: Kennedy, Clarke, Gyepes.
Goals: Cort 25.
Ref: L Probert (Gloucestershire).