Coventry had enjoyed the best of the play in a poor game at the Ricoh Arena, but, with two minutes to go, midfielder Noone dazzled Isaac Osbourne with good footwork to get into the area and calmly rounded goalkeeper Keiren Westwood to slot home his first of the season.
The home side had started well with some attractive attacking play but Plymouth came closest to taking the lead after a 10th minute corner. Marcel Seip's header looked to be heading in but his effort rebounded off the woodwork.
Not to be outdone, the home side had an identical chance during the 18th minute. Danny Fox's corner deflected off a Plymouth defender only to be knocked onto the bar and out.
Both sides passed well but couldn't muster a clear-cut chance. When the Pilgrims finally did have a promising break in the 27th minute, City's Aron Gunnarsson ended the move by taking out Jamie Mackie - he was booked and will miss Coventry's game at Sheffield Wednesday next week.
Coventry then had two chances in a minute, Robbie Simpson headed a Fox free-kick just wide from six yards and then Fox drove a 30-yard shot towards goal, only for Romain Larrieu to palm it away.
Neither side could create a decent chance before the end of the half and it was a same story after the restart.
Twenty minutes of the second half passed without any threat to the respective goalkeepers and both managers brought on players.
One of the substitutes, Freddy Eastwood, nearly helped City take the lead. He won the ball from the Plymouth defence and laid the ball off for Simpson. Simpson's through ball gave Clinton Morrison a one-on-one chance to the right of goal, but his first-time blast went just over the bar.
The tempo waned and the game seemed to be heading for a stalemate, only for another substitute, Noone, to take advantage of a blip in Coventry's concentration and score a goal which put Plymouth in touch with the top six.