It was only the Sky Blues' second league win since August and lifts them clear of the relegation mire, while Plymouth remain rigid in mid-table.
But Peter Reid's men made needlessly hard work of it, allowing the visitors to hit back in a gripping second half.
It took just nine minutes for Coventry to put the memory of Monday night's 3-0 drubbing at Leicester behind them.
The opportunity came from the first corner of the match, which was taken by Michael Doyle. And though Eddie Johnson's header was cleared from the line by Plymouth midfielder Keith Lasley, the ball dropped kindly for Stephen Hughes who smacked home a close-range volley.
Six minutes later, Plymouth presented the Sky Blues with their second dangerous set-piece when David Worrell hacked local lad Gary McSheffrey to the floor.
This time, Graham Barrett took the free-kick and despite intending his low effort as a cross, it somehow bobbled through a mess of players and settled inside the far post.
It wasn't until the 27th minute that the Pilgrims made inroads at the opposite end. Their only real chance of the half came when striker Micky Evans nodded down for David Norris inside the box.
But the 23-year-old, who was clean through, was scuppered by an excellent finger-tip save from home keeper Luke Steele.
However, after a half-time rollicking from manager Bobby Williamson, Plymouth soon halved the deficit.
Evans muscled the ball from veteran defender Richard Shaw 20 yards out, before launching a spectacular dipping volley over his nemesis Steele on 48 minutes.
With Coventry rocking, Plymouth might have notched an equaliser. David Friio, Paul Wotton and Lee Makel worked a cleverly planned free-kick from a central position, but Wotton's disguised shot flashed inches wide.
Substitute Tony Capaldi then wasted a great chance for Plymouth as Coventry sat back for the last 20 minutes. He was blocked on the edge of the area by a last-ditch Louis Carey tackle.
Meanwhile, Dele Adebola – back for the home side after a lengthy loan spell at Bradford – was also causing havoc after being thrown on by Reid.
His mazy run on 77 minutes left Andy Morrell in the clear, but Romain Larrieu blocked with his feet.
And Adebola himself missed a great chance to seal the match when he slid the ball wide of the far post after bursting clear in injury time.