The BT Sport cameras were sent to York Road because of the possibility of an FA Cup giant-killing.
But Pompey failed to follow the script, instead churning out a professional performance to claim a comfortable 4-0 victory.
Ben Thompson broke the deadlock late in the first half, before Oli Hawkins, Jamal Lowe and substitute David Wheeler saw them comfortably through to the second round.
And Kenny Jackett was pleased to see his troops avoid a potential banana skin against National League opposition.
The Blues boss said: “We want to progress as far as we can in this competition and hopefully get to a stage where the big boys enter.
“That’s our aim and to do that you need to cope with – and come through – days like this, so we’re pleased to be in the second round.
“We had good control of the game right the way through, with a lot of quality balls into the box during the first half.
"You need to cope with – and come through – days like this, so we’re pleased to be in the second round."
“You want to get out of sight as soon as possible, but it was always going to be tough because Maidenhead wanted to stay in the game as long as they could.
“Tom Naylor hit the bar and our opponents did then have one moment when they struck the post, but we got the key goal just before the break.
“It was a good cross from Ronan Curtis and Ben finished it – that set up what we did in the second half when we were kicking down the slope and our fitness levels told.
“With the second, third and fourth goals going in, it got more and more comfortable for us and it was a very professional job.”
Attention now turns to Monday evening’s second round draw, but who does Jackett want to see Pompey paired with?
“I don’t mind,” he said. “You always want to be at home but we’ll adapt to whoever we get and do our best to get through.”