The 24-year-old winger smashed in the only goal of the game in the 25th minute to send the Dons through to the second round for the first time in three years.
Macclesfield’s Hamza Bencherif and John Rooney had fierce long-range strikes well saved by Willy Gueret before Gobern put the Dons ahead.
Jermaine Easter’s close-range strike from Stephen Gleeson’s cross was brilliantly saved by Silkmen goalkeeper Jose Veiga but Gobern was on hand to rifle the rebound into the roof of the net from 12 yards.
Veiga saved well from Gobern and Peter Leven, while Gleeson and substitute Jason Puncheon fired just wide as the Dons pressed for a second goal.
Macclesfield rallied late on but Emile Sinclair dragged a good 14-yard chance wide and then lobbed onto the roof of the net from the edge of the box, before substitute Reneil Sappleton fired straight at Gueret eight minutes from the end.