It appeared Rovers' resolute resistance had paid off despite playing 70 minutes with ten men after keeper Gavin Ward was red-carded for handling outside his box.
But when Luke Varney failed to hit the target with his header, Miller directed the ball back across the goal beyond stand-in keeper Ben Hinchcliffe.
The on-loan younger from Preston kept the Cheshire side at bay during a furious finale.
He saved at point-blank from Varney and kept out a Julien Baudet header as Crewe piled on the pressure.
Earlier, Jamaican Ian Goodison had effectively snuffed-out dangermen Varnery and Nicky Maynard.
Then Ronnie Moore's side were able to break to take the lead four minutes after half-time.
Calvin Zola laid the ball off for Danny Harrison, who stroked a right-footer from the edge of the box into the far corner.
Rovers had started the game in less than adventurous mode with their main strikers Chris Greenacre and Gareth Taylor on the bench and they were forced to retreat further in their shell when Ward was caught ought in the 21st minute.
The veteran keeper charged out of his box, handled a Maynard effort after the young striker had been put through on goal.
Ward's deputy Hinchcliffe soon found his box under siege, but Crewe lacked the quality to make a host of half-chances count.
Ryan Lowe went close with a curling free-kick, but it was Varney who was the culprit four minutes before half-time.
After being put through on the left of the box, he lifted the ball over Hinchcliffe and the bar.