A superb goal-saving block by centre-back John Egan to deny substitute Jay Emmanuel-Thomas as injury-time approached typified the visitors’ commitment.
City’s few clear chances came in the second half when Aaron Wilbraham glanced a header just wide, while Luke Ayling and Luke Freeman both fired over from good opportunities.
A low-key first half saw the best opening fall to Gillingham’s Bradley Dack as early as the fourth minute when he shot wide at the far post from Joe Martin’s corner.
Joe Bryan offered the main threat for City, but could not summon up the end product to match some promising approach play. Bryan’s 33rd-minute shot from a narrow angle was smothered by Gillingham goalkeeper Stuart Nelson.
It was the fifth time the clubs had met this season and Gillingham came up with an effective game-plan to nullify their high-flying opponents.