A goal from Yashwa Romeo three minutes from time sparked Slough into a late rally which almost saw them snatch an undeserved equaliser in a goalmouth scramble, but the hosts held on in stoppage time.
It was a game in which Slough never seemed to get going in the heavy rain, but the Rebels had the first real chance of the game when Eamonn McGonigley missed what seemed to be an open goal from a right wing cross.
Lee Chudy was a threat for Slough down the left flank for most of the game, and had Lee Riddell worried as the Slough defender was shown an early yellow card for a shirt-pull.
Slough were forced into some desperate defending as Gosport settled into the game, and Chris Fermie was in the right place in the right time to put in a superb block on the line from Bennett's header.
Gosport continued to dominate and Puckett fired in a shot from 12 yards, but McGonigley blocked the shot for a corner. Slough broke forward but Platt could not get any strength on his shot after Romeo had burst through and squared the ball to him.
Platt had a dip at goal minutes later, but his half volley on the turn flashed across the box with Hutchings scrambling across his goal to collect easily.
With half an hour played and chances few and far between, a moment of controversy arose as James Pritchard suffered a poor challenge, with Gosport defender Birmingham catching the Slough captain above his ankle with studs showing. It looked painful for Pritchard and provoked an angry response from the Slough players, but amazingly the Gosport player was only booked.
Three minutes into the second half, Slough suffered a blow as recent signing Ricky Allaway limped off injured, with Tom Attrell leaving a depleted bench to replace him.
This was to prove very costly for Slough as an otherwise reasonably sturdy looking defence fell apart twice in the space of five minutes. A cross from the right to the back post was missed by Roy Gumbs, leaving Bennett with time and space to control and finish well into the top corner.
Then, on 55 minutes, the hosts cut through the Slough defence again and added a second. A corner was pushed away by Jackson, but the ball was collected cut back into the box to find James Ford in acres of space on the edge of the box, and he duly fired low into the corner.
Gosport were making it look easy with slick passing football on the wet playing surface against a demoralised Slough side. They forced further saves from Jackson through Bennett and Chudy, and again Bennett beat two men down the right and cut the ball back for Ford, whose shot was deflected over as Gosport stayed firmly on top.
Slough offered little threat throughout, but went close through Attrell and Romeo planted a weak header into the arms of Hutchings. However the Rebels managed to pull a goal back as Yashwa Romeo lashed the ball home from 20 yards with a fierce drive which left the keeper partially unsighted.
With 88 minutes on the clock, Slough had finally woken up and Platt fired in a tame shot from the edge as Slough poured forward. Incredibly, one minute into injury time, both Romeo and Pritchard missed from close range as part of a goalmouth scramble as Slough tried, but failed, to score a totally undeserved equalising goal.
The result means a miserable start to November in horrible weather conditions, with Slough needing to play a lot better to realise their ambitions of challenging at the top end of the table.
Gosport Borough Line up
1. Nick Hutchings, 2. Gavin Jones, 3. David Birmingham, 4. Josh Thomas (c), 5. Andrew Puckett, 6. David Waterman, 7. Lloyd O'Neill, 8. Glen Howes, 9. Lee Chudy, 10. Justin Bennett, 11. James Ford. Subs: 12. Vince Rusher, 14. Mark Brown, 15. Nathan Lynch, 16. Adam Shepherd, 17. Aaron Wilson