Dons substitute Andy Yiadom cut the arrears late on but the Railwaymen are in the draw for the second round for the first time in three years.

Harry Cornick was thwarted early on by the boot of home keeper Ian Lawlor but McNeill’s stunning effort edged Crewe ahead in the 12th minute, with the forward spotting goalkeeper Josef Bursik off his line and driving over him into the top corner.

The goalscorer went close soon afterwards when he shot just wide, but the visitors responded and Alistair Smith’s deflected effort flew over before a long-range strike from James Tilley was tipped over by Lawlor.

Steve Seddon’s headed finish from a corner was then chalked off for a foul on Lawlor.

After the break, Lawlor excelled again pushing over a Cornick strike, while at the other end O’Neill’s angled drive was kept out by Bursik.

The in-form McNeill was involved in Crewe’s second in the 62nd minute when his hard-driven low free-kick was parried by Bursik and Thomas followed up to head home.

The Dons pressed in the closing stages with Tilley clipping an effort on to the far post. Yiadom then drove a right-footed finish from 20 yards into the bottom corner.