Despite the defeat, Haringey still lead the table by eight points after defeat for Kingstonian, who have also lost second spot to Lewes, who won 4-3.
Tom Hitchcock gave Harlow a great start with a goal inside 2 minutes.
And then 2 minutes after half-time, Emile Aqcuah doubled the home side`s lead, and although Ralston Gabriel reduced the deficit in the 56th minute, the Hawks hung on for three precious and unlikely points.
Tonbridge Angels ended a run of six games without a win by beating Kingstonian 3-2 at Longmead.
Alex Read gave Angels a 10th minute lead that Joe Turner doubled after 27 minutes.
But two goals shortly before half-time from Dean Inman and Shaun McAuley pulled K`s level.
Recent recruit Chinedu McKenzie grabbed Tonbridge`s winner 19 minutes from time.
Lewes slipped above K`s into second after winning a thrilling Sussex derby by the odd goal in seven against Worthing at the Bibby Financial Services Stadium.
Worthing had a dreadful start when they had Ricky Aguiar sent-off for a rash challenge on Omarr Lawson outside the box with only 26 minutes gone.
Five minutes later, James Hammond gave the Rooks the lead, only for the ten-men to equalise 4 minutes later through Ollie Pearce.
Charlie Coppola restored the visitors` lead right on half-time though and Luke Blewden made it 3-1 within 8 minutes of the second half.
However, recent signing Jalen Jones scored for the second successive game to pull the Rebels back into the game on 71 minutes and then Pearce converted a 90th minute penalty to make it 3-3, only for sub Callum Overton to make it 4-3 a minute later.
But in the 93rd minute, Worthing went down to nine-men when Darren Budd was sent-off for a second yellow card offence and there was no way back but it was great entertainment for a terrific crowd of 1,124.
Dorking Wanderers in fourth dropped two points in a 1-1 draw at bottom-markers Whitehawk.
Nathaniel Pinney gave the struggling Hawks a 65th minute breakthrough, only for Niall McManus to level within 2 minutes.
Bognor Regis Town are fifth after a 2-0 win at struggling Sussex rivals Burgess Hill Town.
Jimmy Muitt broke the deadlock for the Rocks 11 minutes into the second half from the spot and eventually added a second a whopping 9 minutes into stoppage time.
Folkestone Invicta are level on points with Bognor in sixth after hitting five without reply at the Fullicks Stadium against AFC Hornchurch.
It was 3-0 at the break, with Alfie Paxman in the 2nd minute, Johan Ter Horst on 43 and Ian Draycott`s penalty on 45 minutes.
Adam Yusuff immediately added a fourth after the beak and Paxman bagged his second to make it a nap hand just before the hour-mark.
The Urchins day got even worse when they had Ronnie Winn dismissed for a second booking 14 minutes from time.
A 13th minute Walter Figueira goal proved enough for Merstham at the SpecSavers Stadium against Enfield Town, while Corinthian-Casuals edged the derby at King George`s Field against Leatherhead, whose Jazz Wallace gave them a 7th minute lead.
But a Gabriel Odunaike brace after 31 and 61 minutes won it for the hosts.
Brightlingsea Regent enjoyed a good 2-0 win at Potters Bar Town, who finished with ten-men.
penalty just after the break gave the Essex side the lead.
Ten minutes from
time, The Scholars had keeper Berkeley Laurencin sent-off for what seemed to be
jumping the perimeter and collecting the ball!
Hunt doubled his
and Regent`s lead in stoppage time.