The home fans had turned up in party mood ready to celebrate 100 years of football at Kenilworth Road but it looked as though Wolves were going to spoil the party.
But Nicholls' fine strike cancelled out Carl Cort's 25th minute opener and left Luton boss Mike Newell with a smile on his face despite being sent to the stands after an incident with the referee at half-time.
A lively opening period saw both sides seeking to gain the upper hand and it was Wolves that had the first opportunity.
Hungary international Gabor Gyepes rose highest in the Luton area to meet Darren Anderton's precise corner but he could only direct his header wide of the far post.
Luton responded well and Cort had to head clear from under his own bar after Steven Howard had headed Nicholls' free-kick back into the danger area.
It was 17 minutes before either side managed a shot on target but, when it arrived, it needed a superb save from Michael Oakes to prevent Luton taking the lead.
A Sol Davis cross was met brilliantly by Ahmet Brkovic but the Croatian's header was spectacularly turned away by the Wolves keeper.
Just two minutes later it was Luton goalkeeper Marlon Beresford who needed to be at his best to deny Kenny Miller.
The Scotland striker, who has scored three times in two games for his country in the past week, collected Ki-Hyeon Seol's corner and curled his shot towards the far post but Beresford dived away to his left to parry the ball to safety.
But the Hatters' number one was powerless to prevent Wolves taking the lead in the 25th minute. Mark Kennedy was sent clear by Seol's precise through ball and his cross was turned in from close range at the far by post by Cort.
And the big striker could have virtually sealed the game for Wolves in first-half stoppage time.
He was sent clear by another pass from Seol but could only drag his shot wide of the far post and he was made to pay for the miss when Nicholls' third goal of the season earned the home side a share of the spoils.