Nelson returned to winning ways against AFC Blackpool midweek after losing out to Maine Road on Non-League Day.
Defeat at Brantingham Road was the Blues’ fifth in six outings as they let a half-time lead slip against the division’s strugglers.
The Admirals opened the scoring in the 35th minute when Leadbetter guided an exquisite set-piece in to the top corner after Waqas Azam was upended.
But they were clawed back after the break. Matthew Morgan was afforded the time and space to pick his spot from 20 yards to equalise before Michael Burke poked the ball between the legs of Ben Woodhead to make it 2-1.
Leadbetter had two late opportunities to snatch a point, firstly drawing a great save from Ryan Livesey before missing the target when snatching at a first time shot from close range.
However, first half goals from Andrew Bell, Azam and Warren Beattie did the damage at Victoria Park midweek.
The deadlock was broken just minutes later when O’Neill’s mesmerising run and cross from the left hand side was converted by Bell.
Mark Jackson volleyed an effort down the keeper’s throat on the half hour mark, before turning provider for Nelson’s second of the game. Azam traded passes with the striker before sliding the ball home.
And Beattie made it 3-0 with 10 minutes of the half remaining when Beattie controlled the ball on his chest before rifling a volley in to the top corner.
Kurt Willoughby grabbed a consolation for AFC Blackpool when dispatching Marc Taylor’s sumptuous cross.