After only two minutes it was apparent the Walsall defence were in for a long afternoon against the physicality of Mulligan and Delroy Facey.
Facey eased past his marker and crossed to Mulligan, but the striker, making his first league start this season, shot well wide from eight yards.
Gillingham continued to press and were rewarded with their first home goal of the season on 14 minutes.
Andrew Croft crossed to Facey and his flick found Mulligan who lobbed Clayton Ince to score.
Walsall showed little in the opening exchanges but equalised on 20 minutes.
Sean Clohessy was caught out by the on-rushing Martin Butler. The former Rotherham United striker didn't need a second invitation and drove home forcefully from 10 yards into the top right corner.
In the 34 minute Gillingham retook the lead. Craig Armstrong crossed and Facey again he flicked to Mulligan who beat the defence to the ball and lobbed Ince.
With three minutes left in the half Troy Deeney fired against the post.
The second half lacked the same intensity and chances of the first.
Walsall had the better chances but were guilty of profligacy in front of goal.
On 60 minutes Rhys Weston blazed high and wide from seven yards after good work down the right flank.
A minute later Facey could have finished the game after Anthony Gerrard slipped, but the former Bolton striker drove wide from 20 yards.
On 65 minutes Butler broke through Gillingham's defence again and shot powerfully into the top left corner but was denied by a stunning Simon Royce save.
In injury time Paul Hall appeared to have grabbed an equaliser but amazingly Royce somehow managed to claw the ball out of the top left corner.