York held firm for the first 45 minutes, but Jonathan Greening’s red card just before the break was a huge blow.
And the Blues made the most of their extra man, with Ben Davies getting the ball rolling just after the restart.
Marc McNulty then endeared himself to the home fans with a hat-trick to put the result beyond doubt.
But the hosts were not done there and substitutes Conor Chaplin and Ben Tollitt added a further gloss to the already impressive scoreline.
Paul Cook made one change from the side that drew with Carlisle at the weekend.
McNulty was rewarded for his goal at Brunton Park with a place in the starting line-up, as Adam McGurk dropped to the bench.
Pompey showed plenty of attacking purpose straight from kick-off and Gareth Evans’ low cross was just behind the onrushing Caolan Lavery.
The visitors had an opportunity to break the deadlock on eight minutes, but Vadaine Oliver could not make a clean connection with Greening’s quickly-taken free-kick.
It was the Blues causing more trouble, however, and Kyle Bennett had a shot blocked before Christian Burgess saw his header deflected wide.
Lavery then showed great skill to control Bennett’s flick and lift the ball over a defender, but at full-stretch he could only poke wide.
Davies was, as ever, providing plenty of dangerous crosses and one of them was glanced narrowly past the post by McNulty on 14 minutes.
Pompey kept pouring forward and Michael Doyle sent a volley over the crossbar after Minstermen keeper Scott Flinders had failed to hold a corner.
McNulty then had cries for a penalty turned down by referee Iain Williamson after he went down under Eddie Nolan’s challenge.
Flinders was soon called into action once more, keeping out Evans’ angled drive after the winger had latched onto Lavery’s threaded pass.
When York did manage to get forward, the hosts were quick to catch them on the break and one such move ended with Lavery firing wide.
The Blues kept knocking on the door and Bennett was next to go close with a long-range snap-shot that was agonisingly off target.
But the big talking point came right at the end of the half when the visitors were reduced to 10 men.
Greening clattered into Doyle extremely late and appeared to catch Pompey’s skipper with his elbow.
The challenge angered the home side and Williamson quickly put his hand in his pocket to pull out a red card.
York City 0
Pompey were soon back on the attack once the second half started and it took a fantastic save to stop them taking the lead within a minute.
Lavery met Davies’ cross from the right and his header appeared destined for the net until Flinders stuck out a hand to somehow tip the ball over.
But the Fratton faithful did not have to wait long to see their side open the scoring, as a cross from DAVIES somehow evaded everyone on its way into the net.
Doyle’s shot was then well held low down by Flinders as the Blues tried to make the most of their numerical advantage.
And they did extend the lead on 52 minutes when Doyle sent Evans’ low cross back into the box and McNULTY calmly diverted it home.
The rampant Blues soon added a third goal, as McNULTY doubled his tally for the evening by converting Bennett’s cut-back.
Pompey kept pouring forward in search of even more goals and Flinders just about managed to prevent Evans from getting in on the act on 63 minutes.
There was not too long to wait for the fourth to arrive, however, and it was McNULTY who got it, latching onto Doyle’s pass and coolly sliding home to complete his hat-trick.
He immediately left the pitch to a standing ovation, with Davies also departing, as Chaplin and Rommy Boco were invited to the party.
Chaplin immediately looked a threat and sent a free-kick dipping narrowly over before weaving his way into space and seeing a shot blocked by George Swan.
But it was fellow substitute TOLLITT who grabbed the fifth on 80 minutes, surging into the box to convert a fine low cross from Enda Stevens.
CHAPLIN did get in on the act moments later, though, following up to score after Flinders had failed to hold Evans’ effort.
“We want seven,” was the cry from the stands and although the Blues could not oblige, the home fans still left the ground with huge smiles on their faces.
Pompey (4-2-3-1): Murphy; Davies (Boco 73), Burgess, Webster, Stevens; Hollands, Doyle (c); Evans, McNulty (Chaplin 73), Bennett (Tollitt 76); Lavery
Goals: Davies 49, McNulty 52, 60, 71, Tollitt 80, Chaplin 84
Subs not used: Bass, Clarke, Barton, McGurk
York (4-2-3-1): Flinders; Nolan, Swan, Boyle, Ilesanmi; Greening, Berrett (c); Sinclair (Godfrey 56), Morris, Straker; Oliver (Hyde 75)
Sent off: Greening
Subs not used: Ingham, Hare, Tutonda, Turner
Referee: Iain Williamson
Attendance: 13,616 (141 away fans)