It was Gillingham who forced the early pace with Myles Weston heading a dangerous Danny Kedwell cross straight at home 'keeper Seb Brown in the 11th minute.
The opening goal was not far away, though, as Vincelot fired home from the edge of the box in the 23rd minute, having only joined the club on loan from Brighton on Friday.
It was one-way traffic for the remainder of the half, Brown tipping a Matt Fish header over the bar on the stroke of half-time.
Wimbledon rallied after the break with Rashid Yussuff and George Francomb linking up well, the latter forcing Gills 'keeper Stuart Nelson to tip over in the 55th minute.
Francomb continued to prove the most threatening player for the hosts as he fired a 30-yard effort just wide on the hour, before whipping in a teasing cross in the 78th minute which Stacy Long agonisingly failed to connect with.