Ipswich boss Joe Royle received his October award on Friday and, as when he won it in March, Town promptly lost the next match.
The visitors made a lively start and deservedly went ahead on 13 minutes, when Paul Shaw crossed for Rod Wallace to head goalwards.
Home keeper Kelvin Davis tipped the effort onto the bar, but Wallace reacted quickest to dive and head home from close range.
Town were level within five minutes. Shefki Kuqi capped a surging run by picking out Ian Westlake who volleyed home his first senior goal.
There were chances at both ends throughout the half, with neither side defending well, and Gillingham went back in front on the stroke of half time.
Richard Naylor's wayward pass went straight to Andy Hessenthaler who put Mamady Sidibe through and he coolly curled a shot beyond Davis.
Substitute Tommy Johnson had already hit the post with a curling free-kick before Gillingham extended their lead on 54 minutes when Sidibe beat Naylor to the by-line and crossed for Shaw to sidefoot home.
However, Ipswich were not beaten and hit back to level by the 74th minute.
First, Pablo Counago flicked a Jim Magilton cross home before Fabian Wilnis set up substitute Tommy Miller to sidefoot a shot in off the post.
There were no more clear-cut chances until stoppage time when Naylor did well to block Sidibe's shot, and Jermaine Wright slid a dangerous ball away from substitute Mark Saunders.
However, the visitors' late pressure paid off in the final minute of stoppage time when Wilnis lost the ball near his own corner flag and Nicky Southall crossed for Saunders to score with a low angled shot that Davis got a hand to but could not stop.