Harry Redknapp's side struck three times in ten first-half minutes to put the game beyond doubt before the break.
The Sky Blues started reasonably well and could have taken the lead in the 12th minute when Dean Holdsworth met Craig Pead's cross on the volley, but Shaka Hislop was equal to the effort.
The visitors took the lead within a minute as Calum Davenport gave the ball away to Svetoslav Todorov who had a clear run on goal.
The Pompey striker chipped the ball over Morten Hyldgaard but his shot rebounded back off the post and hit Gary Caldwell on the knee before going into the net.
Portsmouth doubled their lead in the 18th minute when Davenport was once again found wanting in defence.
The tall defender lost the ball to Yakubu Ayegbeni who squared for Gary O'Neil. The midfielder passed the ball across to the right for Steve Stone who slotted home from just inside the box.
Kevin Harper made it 3-0 after 23 minutes thanks to another assist from Ayegbeni.
The Nigerian striker beat Pead on the left wing before pulling the ball back for Harper whose well-struck shot was helped into the net by Hyldgaard.
Coventry were struggling to find a way past Portsmouth's defence and were reduced to long-range shots.
Holdsworth turned on the edge of the box just before the break but his effort was well stopped by Hislop.
The home side enjoyed a lot of possession early in the second period but Pompey put the result beyond any doubt in the 67th minute.
Stone crossed from the right and Todorov's back heel found its way through a group of players to Paul Merson.
The former England international, who had a quite game by his own standards, fired goalwards and the ball deflected past Hyldgaard to make it 4-0.