American midfielder Stefani Miglioranzi helped to maintain Portsmouth's early-season challenge at the top of the First Division with his second goal of the season.
But there was a touch of good fortune about his 65th-minute opener which ended Stockport's solid resistance.
Miglioranzi centred from the right into the Stockport six-yard box and it appeared that Stockport fullback Sean Connelly got the last touch to take the ball past goalkeeper Carlo Nash.
Once Stockport had been broken down there was no holding Pompey and there was no denying the quality of the second goal.
Fitzroy Simpson broke down the left past Connelly and Rory Allen stooped to head in his first home goal since his £1million transfer from Tottenham.
Stockport, whose three wins had given them their best start for 50 years, never posed a serious threat.
New signing Laurent D'Jaffo threatened early on with his pace and power and almost opened the scoring with a cheeky volley from 35 yards which dipped just over the bar.
D'Jaffo had a quiet second half and the nearest Stockport came to pulling a goal back came through big striker Brett Angell.
Angell got on the end of a centre from Kevin Copper but the former Pompey junior could not direct his effort on target.
Portsmouth goalkeeper Andy Petterson did not have a save to make and enjoyed a gentle afternoon in the sunshine as Stockport failed to create an opening.
Pompey might have added a couple more near the end but efforts from Allen and Jeff Peron were off target.