Grant made a dream start to his Alex career when he fired home from 25 yards out with just two minutes gone.
Frecklington should have levelled in the sixth minute but he shot wide when it would have been easier to score.
Two minutes later Clayton poked home Ajay Leitch-Smith's cutback at the near post to double Crewe's lead.
But it took the Millers just a minute to pull one back when the unmarked Frecklington's scuffed shot from the edge of the box bobbled past static Crewe goalkeeper Alan Martin.
Frecklington then curled wide before firing a half volley just over the bar while Alex Revell saw a similar effort land inches wide of a post.
Three minutes after the break, Ryan Colclough was tugged back by Claude Davis in the box and Harry Davis drilled home the spot-kick to put Crewe back in the driving seat.
Pringle gave the Millers fresh hope when he struck with four minutes to go and Frecklington finished the job in injury time with a stunning volley from the edge of the box.
- Sports & Recreation
- Ben Pringle