The Hatters looked set to be held by a dogged Walsall side after missing a host of first-half opportunities.
But Nicholls, who saw a spot-kick saved in Town's 1-0 weekend win at Bradford, this time fired home after Neil Emblem had pushed Chris Coyne in the penalty area.
The hosts started well with Coyne and Steve Howard firing volleys over the bar in the first ten minutes before Steve Robinson latched on to Howard's flick-on and drilled wide from the edge of the area in the 11th minute.
Kevin Foley set up Ahmet Brkovic to drill wide in the 18th minute before Rowan Vine twice went close in three minutes.
First he could only shoot weakly at Saddlers goalkeeper Joe Murphy when put in by Howard's pass in the 23rd minute, before, two minutes later, he drilled a cross-shot just out of the reach of the waiting Howard at the far post after Brkovic slipped the ball through.
Brkovic was next to threaten when he turned Simon Osborn in the penalty area in the 28th minute, but saw Murphy smother his close range shot.
Andrew Surman lofted an ambitious 50-yard effort wide for Walsall four minutes before Howard somehow headed over the bar from just eight yards out after Nicholls' 42nd minute corner.
The second half turned out to be as grim as the Bedfordshire weather with both sides struggling to create clear chances.
But when all looked set for a share of the spoils, Coyne fell under Emblem's challenge as he rose to meet a cross in the penalty area and Nicholls coolly slotted home from the spot.