Warnock spared Ross McCormack's blushes as his second-half penalty helped Leeds keep their play-off hopes alive.
Seventy-two minutes had gone when the former England international drilled a spot-kick down the centre of David Forde's goal, with the goalkeeper unable to replicate the first-half penalty save he had made from McCormack.
In the opening stages, Martyn Woolford pushed two half-volleys just wide and with 13 minutes gone, the winger's flick put James Henry clean through on Paddy Kenny's goal six yards out, but he side-footed against the post.
Henry then wasted the chance to put John Marquis clean through, and the home side grew into the game after that, starting with a 17th-minute penalty appeal when Forde appeared to clean up Luke Varney's head as they went for a Warnock cross.
A spot-kick was awarded in the 28th minute, though. The decision came when Byram - through after a superb pass from Paul Green - was hauled down by Woolford, with Mike Jones immediately pointing to the spot. The official was not done however, and halted McCormack's taking of the penalty to order a re-spot. The Scotland striker was far from happy but, after obliging, stepped forward and hit low to Forde's left, with the keeper getting down to save.
Desperate to redeem himself, McCormack retrieved possession and dug out a chip-cross that evaded everyone and floated onto the right post before bouncing back across the line.
If it was starting to seem as though his luck was out, then it was confirmed when he slipped as he tried to tuck in from six yards after a Varney cross, and he was grateful to some errant close-range finishing from Shane Lowry at the other end as the teams went in at the break all square.
The first half had been lively if without goals, but the second half's quality was summed up by Forde's save from a deflected Michael Tonge effort in the 65th minute being the first act to catch the eye.
With the game there for the taking, Millwall tried to seize the initiative and threw on two strikers in the form of Andy Keogh and Nathan Tyson, and the duo nearly combined to open the scoring with 68 minutes gone.
The former, twice an ex-Leeds player, cut in from the right and crossed for Tyson, but Lee Peltier was on hand to deny him and then Keogh on the rebound.
It would prove an vital contribution too as just two minutes later, Dunne tripped McCormack and Warnock made no mistake with an emphatic drive down the middle.
Millwall could have had a penalty of their own after that - Byram looking guilty of handling a Dunne flick - while Varney was denied by Forde, but there would be no more goals.