They lost four wickets for four runs before eventually beating former leaders Southampton Travellers by three wickets at Privett Park.
Both the top two have won seven of their eight completed matches, but Gosport are top by virtue of a marginally better points average - 20.63 to 20.5.
Travellers won the toss and elected to bat, so would have been disappointed with being bowled out for 140 (especially after reaching 55-1).
Wickets were spread around, with two each for Gavin King (2-17), Srinath Nugegoda (2-29), Dale Paternotte (2-30) and Ryan Gander (2-37).
Gosport lost opener Rob Wood for a duck, but skipper King (46) and opener Ross Harrop (33) put on 64 for the second wicket - the highest partnership of the match.
Greg Kitchin (25) and Jackson Todd (17) took Borough calmly to 128-3, whereby three wickets fell for no runs and a seventh fell at 131.
Gander, coming in at No 9, settled any nerves by hitting two boundaries in eight balls as Gosport triumphed in the 37th over.
Gosport’s victory was also great news for Hambledon 2nds, who narrowed the gap on Travellers - only the top two go up - with a thumping victory over Twyford.
Hambledon’s Edward Moger took the individual honours with his maiden Hampshire League century - 120.
Remarkably, that was more than double his previous best score - 58 against Emsworth three years ago.
Hambledon’s decision to bat first was a good one, as Moger and opening partner Will Parvin (37) put on 148 for the first wicket.
Lewis Le-Clercq (28) helped Moger add a further 51 for the second wicket before four wickets tumbled for only three runs.
Joel Eastment’s unbeaten 26 helped Hambledon post a formidable 251-7 (Tom Watson 5-43) off their 40 overs on a day when summer finally made an appearance.
That target was way beyond Twyford’s reach, dismissed for 138 to crash to a 113-run loss at Hunter Park.
Only No 3 Tom Crowley (61 not out) offered much resistance against Mark Le Clercq (3-23), Chris Glanfield (2-13) and Ian Turner (2-26).
Skipper Karthik Muthuraman and Ali Malik shared eight wickets as Portsmouth & Southsea 3rds narrowed the gap on fifth-placed Solent Rangers with a 56-run victory over them at Farlington.
Asked to chase 205 for victory, Solent were dismissed for 148 with opening bowler Muthuraman (4-45) and first change Malik (4-19) doing most of the damage.
P & S’ 204-7 total had been built around some consistent scoring.
Though Danny Fry-Sperring (5) fell cheaply, the other members of the top five all made a start - Tom Wheeler (28), Krishnan Patel (23), Muthuraman (27) and Lenny Field (18).
No 6 Qaiser Naveed then upped the momentum - top scoring with 45 off 27 balls with seven boundaries.
Shan Shajhan, batting at No 7, weighed in with an unbeaten 32 off 18 balls as P & S passed the 200 barrier.