Former Arsenal and Everton striker Jeffers pounced after five minutes of Tuesday night's Crown Ground clash when he latched onto Amine Linganzi's through ball, beat the offside trap and curled the ball into the top of the net.
Number two came after 19 minutes when Luke Joyce found Jeffers, whose initial shot was saved by keeper John Sullivan, with the ex-England international reacting first to head home.
Stanley were coasting and they got their third after 32 minutes when Laurie Wilson's long ball found Will Hatfield for his first league goal of the season.
Wimbledon rarely threatened with their best first-half chance an Alan Bennett header into Paul Rachubka's arms.
Kevin Sainte-Luce hit the post for Wimbledon after the break but Lee Molyneux got a fourth for Stanley after 64 minutes following a neat one-two with Hatfield.