Esh Winning were close to gaining three precious points at Easington Colliery on Saturday.
But they remain at the foot of the Second Division table, with games fast running out.
Esh took the lead through Max Stoker’s fourth-minute strike, but Liam Adamson cancelled that out with a close-range effort for the home side.
Callum Boakes put Esh back in front, a minute before half-time. They scrapped hard to try to hold on to their lead, only for Michael Bulmer to haul Paul Frame’s side level with just three minutes to go.
Esh’s point cut the gap to Ryton & Crawcrook Albion to three points, while Darlington RA climbed a place from third-bottom after a remarkable 5-4 victory against Durham City at Consett.
City took the lead through a Daniel Flounders own goal, but RA turned it around to go 2-1 up through Chris Tarn and Flounders.
Bradley Hird then scored twice to guide Durham 3-2 ahead, only for Glen Donaldson to equalise at 3-3 on the stroke of half-time.
Craig Hennis put Durham back in front on 73 minutes, but Donaldson equalised again, this time from the penalty spot.
The dramatic RA winner came deep into injury time, when Paul New burst through and beat the keeper at the second attempt to win three huge points.
Thornaby, beaten 2-1 by promotion-chasing Stockton Town on Friday, are now third-bottom, six points above Esh Winning, albeit with three games in hand.
Fifth-bottom Willington remain in a struggle, going down 3-0 away to Hebburn Town.
Adam Rundle’s strike and two late efforts from Jason Blackburn saw Scott Oliver’s men home comfortably.
Brandon United, a point better off than Willington, were beaten by 4-1 at on-form Heaton Stannington, whose brilliant surge gives them an outside chance of making the top three.
Lee Johnston gave Heaton the lead and Jonathan Wright made it 2-0 in the 50th minute. United pulled one back through Luke Thompson two minutes later, but goals from Shane Jones and Gary Yates finished them off.
At the top, third-top Billingham Synthonia lost the big game 2-1 when they entertained leaders Team Northumbria.
The visitors went ahead after 13 minutes when John Seaton was adjudged to have handled in the box and was shown a straight red card. Ben Dibb-Fuller, made no mistake from the resulting penalty.
It was 2-0 when Dibb-Fuller scored his second in the 70th minute, with an excellent individual goal.
Though Synners reduced the deficit, with a Nathan Steel strike in the 88th minute, the comeback was too little too late.
Team Northumbria are five points clear of second-placed Stockton Town, who have a game in hand.
The good news for Synthonia was that neighbours Billingham Town also lost, 3-2 at mid-table Bedlington Terriers. Town remain nine points behind Synners, with two games in hand.
Bedlington Terriers went 3-0 up with two early goals from Lee Scott and a Sam Norris strike.
Prolific marksman Craig Hutchinson scored twice, in the 79th and 82 minutes as Town rallied, but Terriers held firm to see out the win.
Elsewhere, Nicky Martin’s hat-trick helped Northallerton win 5-3 at Alnwick and Mark Fitzpatrick netted twice as Whickham triumphed 2-0 at Blyth Town, moving above Durham and Easington into seventh spot.