The bottom-of-the-table side defied their position with a brave performance, although they were never particularly dangerous inside the box.
Neither were the home side in the first-half and after the sale of leading scorer Dean Ashton to Norwich, the Railwaymen are still trying to plug the gap.
Ashton's replacement, Luke Varney, struggled to make an impact and made way for White, whose robust challenge forced Millers keeper Mike Pollitt to spill Anthony Tonkin's corner - allowing the big striker to level the scores.
The contest failed to break into life in the opening quarter of an hour with only a moment of magic from David Vaughan to light up cold winter's afternoon. Vaughan came close in the 19th minute when he made space for a searing low drive from the left side of the box, which missed the bottom corner by a fraction.
But Mullin's 25-yard rising effort in the tenth minute was a decent attempt for the visitors and just missed Clayton Ince's top right-hand corner.
Rotherham grew in confidence and Andy Monkhouse forced Kenny Lunt to clear his shot-cum-cross off the line before Jamal Campbell-Ryce forced Ince to stretch backwards to save his lofted effort.
Crewe had a lucky escape when Steve Foster appeared to be the last man when he brought down Martin Butler on the half-hour mark.
But the centre-half escaped with a yellow card, although his side found themselves behind shortly afterwards when Paul Warne flicked on a short corner into the path of Mullin and the midfielder had time and room to turn and shoot - and while Ince and a couple of defenders did their best to keep the ball out it trickled over the line.
Neil Sorvel attempted to get Crewe quickly back on terms when he hit a iledriver from 25 yards, but Pollitt was up to the task and palmed the ball over.
Butler came close to adding to the Yorkshire side's lead when he scooped his shot from just inside the box over.
And Ince needed to make a great diving save to keep Campbell-Ryce's low 25-yard drive out of his bottom corner soon after the restart.
Pollit then denied Crewe an equaliser when he beat away Sorvel's fierce left-footer.
Crewe lacked punch until Dario Gradi breathed new life into his side by bringing on White and Mark Rivers.
And after White had conjured up the equaliser, Rivers almost stole a winner with a powerful shot Pollitt pushed away before saving White's follow-up.