The Cherries passed the ball impressively throughout the game and opened the scoring in the opening ten minutes through Surridge's first of the afternoon.
The under-18s were putting Portsmouth under pressure and full back Ollie Harfield had a chance well saved by the Portsmouth 'keeper after a run down the left.
The Cherries continued to knock on the door and soon got through once more, as a ball over the top put Surridge through to finish well across the goalkeeper into the bottom corner.
Even at 2-0 down the visitors continued to look dangerous on the counter, especially down the left flank. This led to them pegging one back when the Pompey full-back overlapped and put a ball into the box, which was eventually converted despite some good saves from 'keeper Callum Stanton.
The visitors then pulled level soon after. A half-cleared corner was picked up on the edge of the Cherries' penalty area and fired into the bottom corner past Stanton.
They almost then took the lead soon after, had it not been for a brilliant reaction save by Stanton who got his fingertips to a shot and tipped it onto the near post.
It had been an action-packed opening 30 minutes and there was a feeling that the next goal would be crucial to the outcome of the game.
Unfortunately for the Cherries it fell for Portsmouth, as a corner came into the box and was nodded in by their central defender after 35 minutes.
The under-18s didn't let their heads drop, though. Right-back Connor York bombed forward and nicked the ball into the path of Ben Cooper to shoot at goal, only for a recovering defender to agonisingly clear it off the line.
In the challenge that set up the huge chance for Bournemouth, York took a nasty blow going in fearlessly on the visiting 'keeper. After some treatment on the pitch, he unfortunately limped off just before the interval.
At half time the Cherries found themselves 3-2 down, despite keeping the ball on the deck very well and sticking to the passing philosophy as promoted by manager Carl Fletcher.
In the first real attack of the second half, Portsmouth extended their lead after another stunner from outside the box, leaving the Cherries 'keeper with no chance.
The second half was, however, mostly dominated by the hosts, who kept attacking in a bid to recover the game.
Fletcher's men did get some reward for their hard work eventually, as a penalty allowed Surridge the chance to seal his hat-trick from the spot.
The number 9 stepped up and made no mistake, sending the 'keeper the wrong way to net his third after 60 minutes.
The Cherries then laid siege to the Pompey goal for the final 30 minutes in search on an elusive equaliser.
It was, however, not to come as a combination of the Portsmouth goalkeeper and the post secured three points for the visitors.
The Cherries are back on the road next week as they travel to Exeter City.
Words by Luke Hastings