Two second half goals condemned Dover to their ninth National League loss of the season.
Ahkeem Rose headed Andy Hessenthaler’s side back into the game at the break after Reece Hall-Johnson’s individual strike had put the home side ahead.
However, Wrexham retook the lead in the second half through Fiarce Kelleher before Luke Young sealed victory in added time from the penalty spot.
Chances were hard to come by early on, with it taking over 25 minutes for either goalkeeper to be tested with Hall-Johnson’s shot easily caught by Yusuf Mersin.
Ade Azeez then went close to putting Whites ahead, but after holding off the defenders well, he shot into the side netting.
Shortly after, Wrexham were ahead as Hall-Johnson’s shot from the edge of the box beat Mersin who didn’t see the ball till late.
Whites were almost level immediately through Rose, but after rounding the goalkeeper, his shot was blocked by Theo Vassell.
Rose continued to look dangerous and just before half time he nodded Dover level as he leapt highest to head home Jack Munns’ dangerous free kick.
Wrexham upped the tempo as the second half got underway and almost retook the lead within minutes of the half getting underway, but for Mersin who did well to catch Jordan Ponticelli’s powerful shot.
The Dragons continued to pressurise the Dover defence and retook the lead on the hour mark through Kelleher who flicked the ball on from a cross into the box, finding the net as Mersin was left wrong footed.
Young then looked to double the host’s lead, but his powerful shot from outside the box was well saved by Mersin.
Wrexham sealed victory from the penalty spot through Young in the fifth minute of added time after Mersin took down Kwame Thomas in the box.
Earlier in the day, Hessenthaler named an unchanged side from Whites’ midweek draw against Boreham Wood.