But the League One side were dominated by Blue Square Premier outfit Ebbsfleet for much of the first round tie at the Alexandra Stadium.
Had the Kent side had a cutting edge to go with the neat build-up play of Kezie Ibe and Michael Gash, then they might have recorded a memorable giant-killing.
As it was, Crewe only had two worthwhile attempts on goal yet made one of them count when Donaldson took the pass from James Bailey and nudged ahead of his marker, before despatching a high shot from just inside the box into the top corner.
But the Railwaymen, currently second from the bottom of the table, were very poor for most of the afternoon. It took until the 80th minute before Fleet keeper Lance Cronin was forced to make a save when he went down to hold an angled free kick from Billy Jones.
In contrast the non-league visitors were lively and enterprising up to the edge of the box. In the opening minutes defender Mark Ricketts almost caught out Crewe keeper Steve Collis with a long free-kick and Gash and Ibe forced Collis into agile stops with shots from outside the box.
Fleet boss Liam Daish was convinced afterwards that referee Richard West should have awarded a penalty in the first half when winger George Purcell appeared to be clipped by Crewe midfielder Michael O'Connor inside the box.
Crewe improved marginally after the break and Bailey and O'Connor fired efforts over the bar.
But Ebbsfleet remained in contention right up to the last kick, although they struggled to carve out the one clear chance which could have made a difference.
The closest they went was when Ricketts produced an overhead kick after Crewe failed to clear a corner and the ball veered just a yard over.