Arlesey, who play their football four leagues below the Sky Blues, twice went close to opening the scoring as Chris Marsh looped a shot onto the roof of the net before Ryan Frater headed wide.
However, Callum Ball settled the hosts' nerves when he scored after 28 minutes. Franck Moussa weaved his way through the defence before teeing up the on-loan striker who sent a shot into the top corner of the net from 15 yards out.
The visitors had the better of the early stages of the second half, Marsh going close again before Joe Murphy produced a good save to deny Ben Farrell after 63 minutes.
But Coventry doubled their lead moments later when Cyrus Christie cut in from the right and scored his first senior goal after a neat one-two with Carl Baker.
Jamie Reckord and Moussa both rattled the crossbar afterwards and the Sky Blues added a third late on through Steven Jennings' finish.