Jamie Mackie's fine finish brought Plymouth level two minutes later but Paul Sturrock's side were level for barely a minute as Jamie McCombe's header restored City's lead.
Three minutes later Nicky Maynard grabbed his 50th career league goal in style with a powerful effort to seal the three points.
Plymouth looked full of confidence right from kick-off and could have been in front after only four minutes when Shane Lowry had a chance inside the box but City goalkeeper Dean Gerken made a good save with his feet.
Evander Sno had a long-range shot as City tried to threaten but it was the visitors who continued to make all the running with Ashley Barnes drilling a long-range effort just wide.
Barnes had a better chance minutes later when he was found by Chris Clark's corner but could only head straight at Gerken who made a comfortable save.
City's cause was not helped on the half-hour when Alvaro Saborio was forced off injured and replaced by Louis Carey.
Despite the enforced change the Robins began to improve and Sno had a good chance inside the area but his shot was saved by Romain Larrieu before Paul Hartley sent a long-range effort off-target.
With half-time approaching the home side looked the more likely to take the lead and Danny Haynes dragged a shot wide when he perhaps should have done better.
City picked up where they left off after the break and should have been ahead two minutes into the second half when Jamie McAllister's corner found Lewin Nyatanga who headed over from close range.
Bradley Orr then crossed for Sno who had a header saved by Larrieu before the Plymouth goalkeeper made another good save from Orr minutes later.
Gavin Williams' shot from the edge of the box was comfortably dealt with by Larrieu but City's persistence finally paid off with 17 minutes remaining.
McAllister got away down the left and his cross to the far post found Haynes who slid in for his second goal of the season.
The Robins' joy lasted only two minutes as Rory Fallon played the ball into Mackie and he drilled in a superb effort from just inside the penalty area.
But the game then took another twist as City regained the lead a minute later when McAllister found McCombe who headed in from close range.
Any concerns City had of another Plymouth equaliser were extinguished by Maynard three minutes later when he picked the ball up and fired a thunderbolt past the helpless Larrieu.