Centre-back Atkinson and midfielder Hudson scored the vital goals at Blundell Park on Saturday as the Mariners moved just a point behind their visitors in the table.
Grimsby should have gone ahead in the 27th minute when Hudson beat the offside trap to go clear through on goal but Jake Cole advanced to save at his feet before Michael Coulson fired the rebound into the side-netting.
Grimsby's pressure finally paid off in the 59th minute when Peter Bore collected a clearance from a corner and chipped the ball back in for Atkinson to volley home.
Nick Colgan pulled off two great saves to thwart Mark Hughes as Grimsby held on.
Then, in the third minute of added time, Hudson broke through and fired a shot into the far corner to spark a pitch invasion.