Top Harris scored with the bat, then won three wickets in an 83-point victory at Privett Park.
Harris, at bat at No.4, hit 12 fours and two sixes in a 65-ball 72 after the hosts lost two early wickets.
Captain Lee Harrop hit 25 for the lead before Mark Toogood added a late swing, entering 7th to encircle an unbeaten 39 on 34 balls.
It helped Gosport, who had been asked to beat first, to finish 197-6 on their 40 overs.
With the ball in his hand, Harris struck early in Hythe’s response – dismissing opening opener Tom Gates (10).
Ollie Creal (2-19 on eight overs) knocked out two of the next three wickets, while Hythe’s skipper Tom Richards was knocked out by Charlie Creal.
The latter was then instrumental in putting Gosport in full control, taking 3-24 on six overs as the visitors slipped from 72-3 to 85-7.
There was no way to go back and Harris ended his fine afternoon of work by coming back on the attack and taking the last two wickets to finish with 3-43 against 7.3 overs.
On the fifth Saturday of the 2021 SPL season, Portsmouth and Southsea finally got a game under their belt – but it was a game to be forgotten.
After three of their first four Division 1 games were called off due to waterlogged pitches – the other was dropped after just 12 rounds – the sun set against the Trojans at Stoneham Lane.
The hosts got off to a dismal start after skipper Ben Saunders won the toss and chose to strike – Jack Davies caught the first ball of the game.
Matt Benfield (35) and Ollie Kanavan (14) added 36 for the second wicket before both falling to Syed Mahmood (3-16 on eight overs).
Goalkeeper Alex Davidson (31) impressed before finishing seventh with a P&S score of 110.
It was the first of three wickets to fall in the opening of Syed Agha (3-15) – Jake Peach (1) and Jono Willey (0) the others as the hosts slipped to 110-9.
Dean Lee (24 not released) and Keiron Dunstan (4) added 26 for the final wicket as P&S lifted the Trojans’ target to 137.
Willey gave his team a boost as soon as he fired opener Ed Boyd for a single.
But Nigel Le Bas and No.3 Arsalan Yasin (58) took the game out of P&S reach.
The score was 106 when Saunders fired Yasin, who had hit eight fours and three sixes in a 53-ball stroke.
The Bottom hit Saunders for a winning six-man game on the first ball of the 26th to finish undefeated on 46 as the Trojans marched to victory through eight wickets.