Goals from Ben Thompson, Oli Hawkins, Jamal Lowe and David Wheeler secured victory for the Blues against the non-league side.
The result means the Blues will be in the hat for Monday's second-round draw.
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Here's what fans had to say about Pompey's performance today.
Personally I see it as a job well done, but a job that was expected to be done.
Seeing the scorelines that Maidenhead had been losing by over the past few weeks, I would have been expecting a comfortable win.Â
Part of me especially liked seeing the strong side that Kenny put out, shows ambition to hopefully put together a little run in the cup possibly.
Also very happy to see Ben Thompson get his first goal for the club, he will be beyond key for us this season!
A much improved performance second half. Completely dominated but that should be the case against these teams.
Great to see both loanees Thompson and Wheeler score.
Job done and into the next round.
Pretty one sided game. No joy for the underdogs against League OneÂ Pompey.
Nice paycheck from TV coverage for the National League team.
Very pleasing, professional display from Pompey.
Credit to Maidenhead for their first half performance, unfortunate not to score.
Good cup tie, great respect shown to the opposition and the competition by Jackett.
Professional display from Pompey today and treated their opponents with respect.
Maidenhead did themselves justice.
Onto the next round. Play up Pompey.
WeÂ dominated possession but they had their moments.
4-0 has to be pretty impressive even if it is away to a lower league.
The first half is always the same against non league. They stack 10 men behind ball and hoof it.
In the second half we controlled it. Was a training routine that last half.
Well done Kenny and all the lads.