City moved into the Fifth Round and the last 16 of the FA Vase after an exciting night of cup football in front of a noisy crowd at the Victoria Ground.
A brace from Marco Adaggio overturned the visitors early lead after a Dan Okojie own goal.
City went behind in bizarre circumstances after seven minutes. With time to spare Sam Hall mis hit his clearance from mid way in the City half which fell into the path of Joe Cairnes who put Kyle Carey through on goal, Dan Okojie who was sprinting to catch the striker intercepted only to knock the ball roll past Dan Jezeph.
On 15 minutes it was all level following pressure on the City left. A Dan Okojie pin point cross from the left found the head of Marco Adaggio who finished from six yards out.
Ten minutes later City added a second, which proved to be the winner. Once again a cross was part of the build up, this time from the right with a deep and high ball in from Luke English which was brought down superbly by Sean Brain. His shot from eight yards out bounced off the arm of a defender into the path of Marco Adaggio who bundled the ball over the line to make it 2-1.
The visitors struggled with the pace of the City attack for the remainder of the first half but they nearly drew level when Kyle Carey had a glorious opportunity from a long throw only to be denied by the reactions of Dan Jezeph who produced a fantastic save.
At the other end, City nearly extended their lead through Demetri Brown only to be denied by the ex-Bromsgrove Sporting keeper Reece Francis.
In the second half Coventry had the majority of the ball but there were few decent chances for either side but when they did, City stood firm with Dan Jezpeh punching clear on more than one occasion.
City had a good chance at the other end in the final few minutes and forced a goal line clearance but hung on in front of a vociferous home crowd.