Mulligan turned a cross from new-boy Tyrone Berry into the roof of the net with seconds remaining of normal time to give Mark Stimson's side a share of the spoils.
Former England winger Darren Anderton gave Bournemouth the lead in the 42nd minute with a surging 30-yard run and a low left-foot shot from just inside the area.
Gillingham immediately pressed for an equaliser but striker Simeon Jackson missed a trio of excellent first-half chances.
The best of those came in the 32nd minute when he somehow shot wide from four yards after being set up by Mark McCammon.
Bournemouth, docked 17 points by the Football League earlier in the week, looked to be heading for an important win in their bid to avoid a second successive relegation until Mulligan struck.