Mildenhall dived to his left to keep out a close-range shot from Chris Smith after 70 minutes, and five minutes from time the tall keeper arched his back to palm away a 25-yard drive from substitute Michael Coulson that looked destined for the top corner.
Rovers had the best chance of a scrappy first half after 33 minutes when Lee Brown cut the ball back from the left byline and Eliot Richards fired over from eight yards out.
York often left Richard Cresswell isolated up front but almost scored on the break just before the interval when Tom Platt's fierce shot from just inside the box was palmed around a post by Mildenhall.
The second half saw more dangerous raids from the visitors, while Rovers found it difficult to penetrate a well-organised York defence.
The stalemate ended the Pirates' four-match winning home run but in the end they could feel grateful for a point.