Alfie Rutherford gave the visitors a perfect start by opening the scoring after just four minutes.
Enfield levelled before half-time but the hosts dominated the second period.
Jason Prior and Wes Fogden scored quick-fire goals straight after the break. Substitute Matt Paterson added a fourth with a powerful strike 10 minutes from time.
Just when Petersfield thought their season could not get any worse, they were beaten 4-2 in their Southern League central division one and manager John Robson walked out at half-time.
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They were 3-0 down at half time with Kidlington forward Anaclet Adhiameo scoring a hatrick in the game.
Luke Edwards and Billy Connor scored for Petersfield.
Bognor maintained their one-point lead at the top of the Ryman Premier courtesy of their 1-0 win over Leatherhead at Nyewood Lane.
A 42nd-minute Charlie Moone goal proved enough to secure the vital three points.
Gosport Borough’s woes continued in Vanarama National League South with a 2-1 defeat at Wealdstone.
Aaron Dawson put the visitors ahead in the seventh minute but Wealdstone hit back to score twice after the break. Borough’s misery was complete when Tom Bird was sent off after the break.
Horndean crashed to a 4-1 defeat at Portland United in the Wessex premier. Jack Maloney gave the Deans a 1-0 lead from the penalty spot.
In the second half the hosts took charge to run out comfortable winners.
Baffins Milton Rovers left it late before beating Laverstock & Ford 3-1 in their Wessex division one top-of-the-table clash.
The home side fell behind to a first-half penalty, before Tyler Moret hit a 56th-minute equaliser. Callum Glenn and Ryan Pennery scored at the death to give Baffins a dramatic victory.
The Wessex premier games between Fareham Town and Fawley and Sholing and Moneyfields were postponed due to waterlogged pitches.