Reeves swept in his third goal of the season in the 51st minute to see off the Skrill South minnows, who were possibly unlucky not to secure a replay.
Dons controlled a low-key first half but struggled to create clear-cut chances, with Jason Banton narrowly off target with two long-range efforts.
Dover threatened on the counter-attack and Chris Kinnear fired over a half-volley after a long throw-in had caused panic in the Dons' box, while Sean Raggett headed straight at goalkeeper David Martin.
The Whites started the second half brightly but Reeves put the Dons ahead five minutes after the restart, drilling in substitute George Baldock's square pass first-time from 12 yards.
Baldock then went close with two strikes before Raggett turned Samir Carruthers' low cross against his own post and Patrick Bamford missed an open goal.
Dover rallied late on but Nathan Elder fired over from eight yards and Raggett headed Barry Cogan's free-kick narrowly over the crossbar at the close.