Quick-fire goals within the space of two minutes inside the opening half hour from Sam Vokes and Sam Clucas put the hosts ahead going into the interval.
But the Millers fought back in the second half, with their revival starting when captain Vaulks pulled one back 14 minutes after half-time when he headed in from a corner.
And the South Yorkshire club were level after 73 minutes when substitute Crooks bundled in from close range.
Enjoying the better of the early play, Paul Warne's Millers saw strikes from Anthony Forde and Richie Towell go just off target.
Stoke were ahead after 27 minutes when forward Vokes met Ashley Williams' pinpoint cross from the right to head unmarked past goalkeeper Marek Rodak and into the bottom-right corner.
And Nathan Jones' Potters doubled their lead two minutes later when James McClean's low ball from the left was flicked into Clucas' path by Vokes inside the box, with the midfielder driving his left-footed shot into the top of Rodak's net.
Up the other end, home stopper Jack Butland was forced into action, keeping out low attempts from distance by Rotherham duo Jon Taylor and Vaulks.
As the opening half drew to a close on a windy spring afternoon in Staffordshire, Vokes tried his luck to double his tally, though his right-footed strike was turned behind by Rodak.
After the break, Rotherham pushed to get back into the contest and Butland made a sprawling low stop down to his right to push Clark Robertson's header from Forde's cross away for a corner.
With 59 minutes on the clock, the visitors earned a lifeline when Vaulks directed his header from Forde's right-sided corner across goal which beat Butland.
Buoyed by halving the deficit, substitute Joe Newell profited from a short corner routine from the right to thump a dipping attempt on the edge of the box which Butland did well to tip over.
Rotherham's equaliser came with 17 minutes remaining as Vaulks' long throw was flicked on by Semi Ajayi before falling to Crooks, who turned the ball past Butland from a matter of yards.
Crooks almost completed the turnaround late on, but he was denied by Butland's superb stop, with the England international springing to his right to tip the ball over.
The result sees Rotherham remain in the relegation zone, a point behind Wigan.