Matt McClure slammed in his ninth goal of the campaign with five minutes left to deny the hosts a return to the summit of League Two.
But in injury time, the 19-year-old Archer - on loan from Tottenham - was placing the ball to take a goal kick when the supporter entered the field and leapt on his back.
The fan was quickly apprehended by a steward and led away at the Priestfield Stadium.
Wycombe boss Gareth Ainsworth told Sky Sports: "Some people give the rest of the Gillingham fans a bad name.
"I don't want to comment too much, but everyone is okay in there."