The visitors, tipped by many for the drop, took a first-half lead, but Town hit back through Richard Naylor and Bowditch to seal only their second first day win since the 1999-2000 season.
Former Norwich forward Iwan Roberts, booed throughout by the home fans, marked his Gillingham debut inside the first minute when he clattered into Drissa Diallo in an aerial challenge and was booked.
The visitors posed the first threat on nine minutes when left-back John Hills crossed from the by-line and Matt Richards was well-placed to head away from close to the line.
Bowditch saw an angled volley well held by Gills keeper Steve Banks before an ambitious overhead kick by Darren Byfield flew wide for the visitors.
Ian Westlake saw a volley blocked by Banks before Gillingham went ahead on 23 minutes, when Town conceded possession, Byfield raced clear and crossed for skipper Paul Smith to fire beyond Kelvin Davis.
Byfield saw an effort easily gathered by Davis before Town levelled on 35 minutes, debutant Kevin Horlock's corner to the far post headed down and beyond Banks by Naylor.
Gillingham should have replied immediately, but, much to the home crowd's delight, Roberts planted an unmarked header from Chris Hope's cross over the bar from five yards.
Banks denied Miller with a diving save in first half stoppage time, but 30 seconds after the interval, Bowditch placed a sidefoot volley beyond the visiting keeper after collecting a deep Drissa Diallo cross.
Banks denied both Matt Richards and Pablo Counago as Town searched for a third, while Byfield sent one effort wide and Davis made an excellent save from another as the hosts hung on for three valuable points