Crawley, under new boss John Gregory, looked the more likely scorers in the first half and Mildenhall had to be at his best to beat away a fierce volley from Mark Connolly shortly before the break.
The tall goalkeeper had also done well to save a 15th-minute header from Gary Alexander, while at the other end there were few alarms for Crawley keeper Paul Jones.
Oliver Norburn hit the crossbar with Rovers' best effort - a right-footed volley from 20 yards just before the hour-mark - and Jones later had to dive full length to keep out a long-range effort from Eliot Richards.
But Crawley looked dangerous throughout and Mildenhall continued in top form, saving from Dannie Bulman and at the feet of Joe Walsh in the second half.
John Ward's Rovers battled tenaciously though and in the end were worth their replay.