They couldn’t take advantage with late, late drama at Braintree Town.
Paul Doswell must have thought it was job done 3-2 up in the 95th minute at Cressing Road but Rhys Murrell-Williamson had other ideas, completing his hat-trick in the dying seconds.
Bath City joined them on 36 points, leaving it very late themselves to in 2-1 at Eastbourne as Alex Hartridge won it in the 92nd minute.
Dorking Wanderers are in the hunt now too - a fine 3-2 win at Maidstone United, Jason Prior completing the fightback - a third win a row for Marc White’s men.
Dulwich Hamlet lost super fan Mishi Morath this week and there was no doubt their much-needed 4-1 win at Hungerford was for him. Danny Mills wrapped up the points after Dylan Kearney got things going with his first goal for the club.
St Albans needed a win too and they got it somewhere not many expected.
A valiant 1-0 success at Weymouth lifted the Saints off the bottom of the table.
Tonbridge boosted their survival chances with a 1-1 draw at Hemel but they were denied a win by a late home leveller.
Concord Rangers are up to ninth as they held firm to win 1-0 at Dartford. A Joel Nouble penalty took the points home to Essex.
Chippenham Town gave their season a boost, winning at home to Chelmsford - David Pratt and Curtis McDonald scoring the goals.
National League South results:
Braintree Town 3-3 Havant
Chippenham 2-1 Chelmsford
Dartford 0-1 Concord
Eastbourne 1-2 Bath City
Hemel H 1-1 Tonbridge
Hungerford 1-4 Dulwich
Maidstone United 2-3 Dorking
Weymouth 0-1 St Albans