The Sky Blues got back to winning ways thanks to a first half double by Michael Doyle and a superbly worked Jay Tabb goal early in the second half.
After a slow start, Doyle smashed two goals in the space of seven minutes at the end of the opening period with Tabb's strike effectively ending the tie before Steve MacLean scored a late consolation goal for the visitors.
In the second minute referee Richard Beeby showed Plymouth striker Jermaine Easter a yellow card after he tried to con the match official into awarding a penalty. Scott Dann did not get much on a back header to Kasper Schmeichel and Easter nipped in to knock the ball past the City keeper before taking a dive. Thankfully Beeby was not fooled and instantly booked the Argyle forward.
In the 12th minute the visitors missed a golden opportunity to take the lead. Gary Sawyer attempted a shot from 25 yards but miscued so badly it appeared it would go out for a throw-in. However, with City's defenders napping, Jim Paterson reacted quickest and squared for Steve MacLean who somehow missed from five yards out with the goal at his mercy.
City had failed to stamp their authority on the tie as they had in recent home encounters but by the half hour mark had started to show more as an attacking outfit with Robbie Simpson - recalled to the starting line-up in the absence of Leon Best - looking lively up front.
But the opening goal came from midfield after City had showed plenty of composure in possession of the ball. A Jay Tabb cross from the right found its way to Michael Doyle at the far post via a good flick-on by Simpson and the Irishman fired a crisp volley past keeper Luke McCormick to give the Sky Blues a35th minute lead.
Having waited so long for a goal, you could see the pressure lifted from the shoulders of the City players and by the 42nd minute it was 2-0, with Doyle again the scorer. Argyle skipper Paul Wotton sold Russell Anderson short and Jay Tabb nicked the ball to race clear of the Plymouth defence. The energetic midfielder reached the penalty box, looked up and delivered an inch perfect pass for Doyle to slot home from six yards out.
The game was nearly out of sight in the 52nd minute when City came close to a third, defender Scott Dann's accurate header cleared off the line by a Plymouth defender.
Just after the hour mark Chris Coleman made his first change, bringing on Kevin Thornton for Julian Gray and switching to a 4-5-1 system, with Simpson playing the lone striker role.
And the switch did not stop the Sky Blues from playing some excellent football going forward, with Jay Tabb making it 3-0 in the 66th minute with a superbly worked goal.
Simpson did brilliantly to win possession on the left and play the ball back to Tabb, who cut inside, fed Thornton and then received the ball back again before slotting calmly past McCormick.
The goal prompted a triple substitution from a clearly disgruntled Paul Sturrock who had seen his side's hopes pretty much disappear completely after City went three goals clear.
In the 82nd minute Steve MacLean pulled one back for the visitors when he smashed into the roof of the net from close range after the Sky Blues had failed to clear their lines.
But City remained in control and in the dying stages loan signing Zavon Hines was introduced in place of Michael Mifsud, although the youngster had little time to impress, despite the referee mysteriously awarding five minutes of stoppage time at the end, which the visitors failed to take advantage of.
Coventry: Schmeichel; Fox; Ward; Hughes; Doyle; Osbourne; Mifsud (Hines 87); Tabb; Simpson; Gray (Thornton 61); Dann. Subs (not used): Marshall; Hall; Duffy
Booked: Simpson (79)
Plymouth: McCormick; Connolly; Paterson: Clark (Abdou 67); Teale; MacLean; Wotton; Sawyer (Mackie 68); Seip; Anderson (Timar 67); Easter. Subs (not used): Nalis; Jutkiewicz
Booked: Easter (2); Sawyer; MacLean (32); Paterson ( 71)
Referee: Mr R Beeby
Attendance: 18,775 (1,835)
