Pompey Reserves exited the the Hampshire Senior Cup after falling to a 7-0 loss to the Hawks at Westleigh Park.
A youthful Blues side showed plenty of heart and endeavour but the hosts’ experience ultimately proved too much.
Matt Casey was the only first-team player involved and skippered the side, although Leon Maloney, Bradley Lethbridge Josh Flint and Eoin Teggart – who have all featured in this campaign’s EFL Trophy – also started.
Manager Kenny Jackett also watched on form the stands.
Hawks went close in the third minute when Rutherford’s stooping header went well wide of the target.
The hosts did have the lead four minutes later, however. Pompey failed to clear a bobbling ball and Fratton youth product Tarbuck crashed home a half-volley.
But the Blues did make a decent response, with Charlie Bell’s deflected effort in the 19th minute just going over the bar.
And three minutes later Eoin Teggart cut a ball back for Harry Anderson, although he dragged his first-time shot wide.
Pompey showed plenty of composure on the ball, but ultimately the Hawks’ physicality started to dominate.
Josh Taylor gave visitors a scare six minutes before half-time when he dragged an angled effort wide.
But three minutes from the break, Rutherford doubled the Hawks’ advantage when he drilled home into the bottom right-hand corner.
And they almost added a third moments later when Rutherford teed-up former Pompey defender Magri, but he failed to keep his effort down.
It took less than 60 seconds into the second half for Doswell’s men to extend their lead. Substitute Jonah Agunga powered his way into the box before cracking a left-foot shot that went through Petar Durin in the visiting net.
Then Keswell thought he’d given the Hawks a fourth in the 55th minute when he headed home with aplomb, but he was flagged offside.
Home keeper Kingsley Latham was forced into his first save of the evening moments later. After Lethbridge was brought down 25 yards from goal, Maloney’s free-kick beat the wall but Latham pushed the effort around the post.
The home side’s fourth goal arrived fortuitously in the 61st minute when Chris Paul's long-range effort took a wicked deflection and left Durin helpless.
Liam Daish’s side did nearly have a consolation goal on 68 minutes when Lethbridge charged down Latham’s clearance, only for the ball to roll the wrong side of the post.
There was little surprise when the Hawks bagged a fifth, though, with Aguga finishing into an empty net after Durin parried Tarbuck’s cross.
Tarbuck had his second four minutes later when he dinked an effort over the onrushing Durin.
Then Agunga rounded off his hat-trick with two minutes remaining with a fine finish from the edge of the box.
Pompey: Durin, Dnady, Casey, Rew, Maloney, Bridgman (Brook 46), Bell, Flint, Teggart (Kelly 46), Anderson (Jae-Lee 61), Lethbridge.
Subs not used: L Pitman, Robb.