The Manchester United winger stabbed home a cross from Sylvan Ebanks-Blake in the 16th minute to extend the Pilgrims' unbeaten home run this season to eight matches.
Goalscorer and provider were at Old Trafford together for four years, as well as spending a joint loan spell at Belgian club FC Antwerp, and their understanding clearly showed.
Martin, signed on a three-month deal a fortnight ago, announced his arrival at Home Park when by taking Ebanks-Blake's pass with a neat bit of skill and firing off a shot that City goalkeeper Andy Marshall just stopped.
The Taunton-born flankman then went one better when he combined again with Ebanks-Blake, who curled in a right-wing cross which Martin poked home at the near post for the game's only goal.
Argyle should have wrapped the game up before half-time as they created a succession of chances.
David Norris fired over from 12 yards when well placed, but went closer when he hooked a shot over his shoulder from the edge of the penalty area.
Martin volleyed another Ebanks-Blake created chance goalwards, only to be thwarted by a finger-tip save from Marshall, who was badly served by his defence throughout.
Coventry were a much better prospect after the interval, but it was the home side who went closest to adding to the scoreline.
One free-kick from Hungarian international Peter Halmosi had Marshall scrambling at the foot of his left-hand post, while another set-piece shot saw the veteran goalkeeper clutch an on-target shot to his chest.
The Ebanks-Blake-Martin partnership nearly reaped further dividends before Coventry came close to stealing a point in time added on, when Julian Gray's lofted free-kick was missed by Argyle goalkeeper Luke McCormick.
The ball took the merest of touches off Kevin Kyle's head but, fortunately for Argyle, grazed the foot of the post as it went just wide.