Bournemouth were docked the points by the Football League after coming out of administration and it looked as if they would begin the new season with a win.
But then Mulligan, an 87th minute replacement for Adam Miller, turned in a low centre from the right by Gillingham's other substitute Tyrone Berry.
Gillingham should not have needed Mulligan to rescue them, but striker Simeon Jackson had an off day in front of goal.
Jackson spurned three comfortable first-half chances, the best of those in the 32nd minute when he somehow struck a shot wide from four yards.
Bournemouth goalkeeper Shwan Jalal also made a good save from Jackson and it was the same in the second half as the Gills pressed forward without success.
The lacklustre Jackson dragged a shot wide in the 58th minute and Mark Bentley headed over from close range when it looked easier to score.
Patched up Bournemouth, with only 16 professionals, fought gallantly and took the lead in the 42nd minute with a vintage piece of skill from veteran Darren Anderton.
Anderton, now 36, ran 30 yards through the heart of the Gillingham defence before unleashing a low left-foot shot which gave goalkeeper Simon Royce no chance.
Anderton faded in the second half as Gillingham threatened to take command, but Jo Kuffour had the chance for a second only to snatch a decent chance in the 55th minute.
Gillingham defender Simon King and big striker Mark McCammon were booked for fouls, as was Bournemouth striker Brett Pitman who was later forced to leave the field with a head injury after a collision.