Dack took advantage of a series of Morecambe mistakes to flash a shot past Barry Roche from six yards out to level the scores in the 52nd minute after Jack Redshaw had given the home side a first-half lead.
Redshaw scored for the fifth time in six games with a close-range finish just before half-time after Stewart Drummond's right-wing cross had been knocked into the box by Gary McDonald.
The visitors went close to taking the full three points when Matt Fish flashed a shot inches over the bar and Dack went close to a second with a flicked header that sailed just wide of a post.
Redshaw went close to giving Morecambe the lead after 18 minutes when he volleyed over after a poor defensive header from Fish.
The diminutive striker also drilled a shot wide after Gillingham's Michael Richardson almost put the ball into his own net when looking to divert a Will Haining cross.