Billy Logan finally broke the deadlock at Long Eaton by giving the leaders the lead on the hour-mark.
But they dropped two points at the end when Shay Wiggins equalised with only 3 minutes remaining.
A 25-yard screamer from Brighouse`s Danny Nadiole knocked the stuffing out of Liversedge, with Ernest Boafo and Ryan Hall adding to the scoreline before James Hurtley had the final word in the local derby.
Scarborough Athletic are only a point further behind after beating Arnold Town 3-1 at Queensgate.
Ryan Blott bagged a brace for Boro in the 36th and 75th minute with the experienced Tony Hackworth sandwiching the other on 65 minutes after Henry Sibenge had equalised for the Eagles 5 minutes before the break.
Worksop Parramore are fourth after a 2-1 win at basement side Winerton Rangers.
Tom Roebuck gave Parramore the lead on the half-hour mark. Blake Freeman levelled 5 minutes before half-time, only for Scott Bates to score what proved to be the winner for the visitors 6 minutes into the second half.
Goals from Richard Patterson and substitute Joe Thornton ensured that Staveley Miners Welfare brought three points back from East Yorkshire against Hall Road Rangers, despite a pretty awful performance for the first hour.
Martin Mathers hit a hat-trick to help Thackley beat Armthorpe Welfare 3-0.
Mathers` goals came in the 25th, 31st and 52nd minutes.
Pickering Town won by the same scoreline at home to Glasshoughton Welfare, but the goals were shared out between Liam Salt after 11 minutes, Liam Shepherd on 27 and Joe Danby just after half-time.
And Maltby Main also won 3-0 at home against second-bottom Lincoln Moorlands Railway, courtesy of goals from Adam Houghton after 14 minutes, a Craig Gladwin penalty on 48 and Brian Cusworth 10 minutes later.
Heanor Town edged out Parkgate by the odd goal in five.
Richie Holmes have the home side a 36th minute lead, but two goals in 2 minutes shortly after the break from Simon Hickey and Lee Hill gave Gate a 2-1 advantage.
Nathan Benger equalised on 63 minutes and then Jordan Hall won it for Heanor with 8 minutes to go.