On a chilly day at Wide Lane, the visitors opened up a commanding lead after just 24 minutes through Owen Barnes, Will Hartley and Chris Bollom.
The students hit back after the restart, equalising with three goals in 15 minutes. But within two minutes of the leveller, Portsmouth were back in front when man of the match Hartley netted his second.
Hartley set up Stuart Avery to make it 5-3 with five minutes remaining, before the University had the last say from a penalty corner.
Portsmouth 2nds were unable to close the gap on fourth-placed Southampton University 2nds in Division in Division 3 South.
They took the lead against the students through Adam Nicholls, following three consecutive penalty corners, but were eventually beaten 4-1.
Portsmouth 3rds turned in one of their best displays of the season at third-placed Alton 3rds in Division 5 South.
Depleted due to a succession of late drop outs, they travelled without too many expectations - so were delighted to be leading 3-1 in the second half.
Alton, though, hit back to force a 3-3 draw.
Portsmouth led early on through man of the match Tom Love before the same player turned provider to set up Gary Bull for a tap-in.
Alton converted a short corner on the stroke of half-time, but Portsmouth extended their lead when Alex Love scooped a pass to his brother Tom who netted his second goal with a spectacular volley.
Alton quickly responded with a cheeky short corner flick over Matt Forrest, and levelled from a short corner with only a minute left.
Portsmouth 4ths survived a first half green card for keeper John Arnell to beat Hamble 3rds 5-2 in Division 1 Solent.
Hamble twice led before half-time with Karl Young and Tom Hughes twice levelling.
The game continued to be end to end in the second half but Bryan Hodges, Ivan Boswell and Peter Wingate saw Portsmouth emerge triumphant.
Charlie Boswell was awarded man of the match for showing great skills and composure.
Portsmouth 5ths are on the verge of the Division 2 Solent title after thrashing second-placed Lavant 7-0.
Teddy Bissett opened the scoring and it was 3-0 at half-time after the ball deflected off Alex Jarrett’s stick and in off a defender’s stick.
The highlight of the second period was Portsmouth’s sixth goal, scored by Jamie O’Shea.