scored either side of half time as the Gills made it three league wins out of four against Wigan Athletic at the MEMS Priesfield Stadium on Saturday.
Dack opened the scoring on 37 minutes after good work from Jordan Houghton and Rory Donnelly, and then secured the victory for the hosts with a late penalty. The midfielder has now scored five goals in five games across all competition this season.
Manager Justin Edinburgh named an unchanged starting XI from Tuesday's brilliant win at Bradford City, albeit with striker Cody McDonald
returning from injury to make the bench for the first time this season.
And the Gills started as they finished in Yorkshire in mid-week, as Dack forced Wigan goalkeeper Richard O'Donnell into a save within the first 40 seconds.
Four minutes later, Deji Oshilaja scuffed wide from close range after the Latics had failed to fully clear a corner.
Brennan Dickenson came close with a 30-yard volley after a quarter of an hour, and Luke Norris had an effort blocked as the hosts increased the pressure on the former Premier League side.
And just as the half looked like it would end goalless, the Gills took the lead on 37 minutes.
Having dispossessed Reece James in the Wigan half, Jordan Houghton played in Rory Donnelly, who unselfishly found an unmarked Dack, allowing him to coolly slot home.
Athletic's best chances of the half came when Chris McCann shot just over from Michael Jacobs's free-kick on 19 minutes, and Will Grigg saw his half volley comfortably saved by Stuart Nelson
Houghton continued to prove a menace for James in the opening minutes of the second half, as the on-loan Chelsea midfielder once again dispossessed his man, but from the resulting pass Josh Wright shot straight at O'Donnell. Only a brilliant last-ditch challenge by Craig Morgan prevented Norris from adding a second when through on goal seconds later.
Nelson continued his brilliant run of form on 55 minutes, as he somehow kept out Grigg's goal-bound effort at his back post. From the resulting Gills break, Norris couldn't have got any closer to a second, as his 20-yard effort hit the outside of the post.
Norris volleyed just wide from an acute angle on the hour mark, and Donnelly couldn't divert his header from Dack's free-kick goal-bound with 13 minutes remaining.
However, the Gills got the second goal they throughly deserved eight minutes from time. Former Gills loanee Donervon Daniels fouled Dack in the box, and the in-form midfielder confidently converted the penalty.
The visitors' day was summed up when Jacobs and Sean Murray both came agonisingly close to a consolation in stoppage time.
The Gills travel to Birmingham on Tuesday for their second round Capital One Cup tie, and are on the road against next Saturday against Peterborough.
Gillingham: Nelson, Jackson, Egan, Oshilaja, Dickenson, Hessenthaler, Dack, Wright, Houghton, Donnelly (McGlashan 90) Norris (Williamson 72)
Unused subs: G Morris, Garmston, Ehmer, Oldaker, McDonald
Wigan Athletic: O'Donnell, McCann, Morgan, Daniels, McNaughton (Kenny 43), Jacobs, Junior (Murray 45), Perkins, James (McKay 78) Davies, Grigg
Unused subs: Jaaskelainen, Barnett, Pearce,Power, McKay