The gap at the top of the Vanarama National League South table is now just two points after leaders Dartford were beaten, but second-placed Hampton & Richmond Borough dropped two home points.
Dartford suffered a 2-1 defeat to a now fourth-placed Chelmsford City side at Princes Park on Saturday.
The Darts were leading after 33 minutes, thanks to a wonder strike from Ryan Hayes.
But an 86th minute penalty, converted by sub Kudus Oyenuga, and a goal direct from a corner by Taylor Miles in stoppage time produced a dramatic turnaround.
Hampton will be kicking themselves for dropping two Beveree points to bottom-markers Whitehawk, despite the Sussex side`s recent improved form.
The Hawks took a 34th minute lead through Elliot Benyon.
And the Beavers grabbed an equaliser immediately after half-time when Hawks` keeper Dan Wilks carried the ball over the goalline after a corner.
But the home side had to play the final 30 minutes or so with ten-men after
Charlie Wassmer was shown a second yellow card and was sent-off for a two-footed lunge on Benyon.
Havant & Waterlooville moved to within a point of Hampton and three of the Darts after winning 3-1 at Tatnam against another of the strugglers, third-bottom Poole Town.
Things couldn`t have started much worse for the Dolphins as they had goalkeeper Nick Hutchings sent-off after just 18 minutes for bringing down Paul Rutherford.
Sub Tom Rees` first job was to pick Rory Williams` spot-kick out of the back of the net.
But the ten-men pulled back on level terms 5 minutes before half-time through Warren Bentley.
And they held out until 6 minutes from time when Theo Lewis made it 2-1 and Wes Fogden added a third in stoppage time.
With St Albans City`s game at Hungerford Town being postponed, Hemel Hempstead Town had the opportunity to move up to fourth but were beaten 4-1 at Marsh Lane by an Oxford City side who are now seventeenth, four points above the drop zone.
City took the lead against the run of play on 16 minutes when Reece Fleet was on hand to turn home.
Moments later former City keeper Laurie Walker was adjudged to have handled outside his area and was shown a straight red card.
A scramble in the box on 25 minutes resulted in City’s second goal with Christian Oxlade-Chamberlain forcing the ball over the line.
City looked fairly comfortable in the second half, but they were sweating on 73 minutes when sub and new signing Darren Ward headed home, but things looked much more comfortable 5 minutes later when Oxlade-Chamberlain found Godfrey Poku spare to stroke home.
There was still time for lively debutant Sam Nombe to join the party as he fired a shot into the top corner for City’s fourth in the 84th minute.
Truro City and Braintree Town, in seventh and eighth respectively at the start of play, were also beaten on Saturday – and both at home.
The White Tigers lost 3-1 at Treyew Road to a Wealdstone side now in twelfth spot, but only five points behind their hosts with a game in hand.
The Cornish side took an early 8th minute lead through Aaron Lamont.
And they held that advantage until 3 minutes into the second half when David Pratt equalised.
Pratt grabbed his and The Stones` second virtually straight from the kick-off and Danny Green made the points safe with a third in the 66th minute.
Braintree lost 2-0 at home to a Bath City side who are now just a place and a point behind them in the table.
City`s opener came after 23 minutes when Anthony Straker’s effort was parried by Nathan McDonald, but Nat Jarvis was on hand to tuck the ball away.
And 10 minutes later, they doubled their lead when Jack Compton curled home a lovely effort round McDonald.
Bath`s neighbours Weston-super-Mare are just a couple of points behind them with two games in hand after beating a Concord Rangers side who had lost only once in seventeen league games.
Jacob Cane celebrated signing his new deal with the Seagulls by grabbing the only goal of the game in the 16th minute at the Woodspring Stadium.
Second-bottom Bognor Regis Town look in deep trouble and are now nine points adrift of the safety-mark after losing 1-0 at another of the strugglers, fellow newcomers Chippenham Town.
The Bluebirds moved three points clear of the bottom three, thanks to a thoroughly miserable day for the Rocks, who had Calvin Davies dismissed 6 minutes before the break and saw Dan Beck concede an own goal 5 minutes into the second half.
But it was a much better day for Gloucester City, who moved out of the relegation places after a best-of-five win at Park View Road against Welling United.
It was goalless until the 58th minute when Karnell Chambers gave the Tigers the lead.
That lasted barely 2 minutes though as Bradley Goldberg equalised.
But a Christian Nanetti own goal restored City`s lead in the 75th minute, only for Goldberg to level from the spot 7 minutes later.
Ed Williams won it for the visitors though as stoppage time ticked in.
East Thurrock United and Eastbourne Borough played out a low key stalemate at Rookery Hill in the day`s other game.