Sugden, who has been doing physio work at the University of Huddersfield, looks leaner and stronger than before and out-muscled the Exeter defence to register goals on five and 38 minutes.
The opener was a powerful shot after City defender Dean Moxey's weak headed clearance had been knocked back into the box by Halifax's Steve Bushell, with the ball bouncing off an Exeter player to land at the unmarked Sugden's feet.
The clincher was a header from Matt Doughty's free-kick which Grecians keeper Paul Jones managed to get his fingertips on to, but could not prevent it crossing the line before any covering defenders could react.
Sugden could have polished off a fine hat-trick after the break but Jones beat away the frontman's curler in the 60th minute when Bushell again knocked the ball back into the box following another poor defensive clearance.
Exeter, missing 13-goal top scorer Lee Phillips through injury, had half-chances but never really threatened Halifax's goal despite dominating possession throughout the second half in bitterly cold conditions on a pitch that cut up badly.
The closest City came to scoring was just before Town extended their lead. Halifax keeper Jon Kennedy dropped a cross from Andy Taylor on 32 minutes but recovered in time to stop Paul Buckle's goalbound effort crossing the line.
Halifax still have the only unbeaten home record in the Conference and look well-placed to reach the play-offs. It was their fourth straight win while Exeter, who were strong top-five contenders until recently, have now lost four of their last five matches.