With second-placed Hampton & Richmond Borough and third-placed Havant & Waterlooville both having the afternoon off due to waterlogged pitches, Dartford had the chance to extend their advantage at the top.
But the battling Bluebirds twice came back from being behind to earn a point.
Alfie Pavey gave the Darts the lead after 39 minutes – the scoreline at the interval.
But just six minutes into the second period, Dean Evans popped up with Chippenham`s equaliser.
Pavey`s 20th goal of the season on the hour-mark restored the Darts` lead, only for Nick McCootie to level on 67 minutes for what proved to be the final goal of the game.
Braintree Town could have moved into second had they won at Cressing Road against Hemel Hempstead Town.
However, the Iron were hit by a last-gasp sucker punch to lose 2-1 to a now fifth-placed Tudors.
Phil Roberts put the home side ahead in the 18th minute.
Hemel hit back 5 minutes before half-time with an equaliser from Spencer McCall and after a scrappy second half in worsening conditions, the visitors grabbed the winner through Ebby Nelson-Addy in time added on at the end of the game.
Hemel moved above Truro City, who slipped to a 3-2 defeat to a resurgent Whitehawk at the Enclosed Ground.
The Hawks are still a massive 12 points behind fourth-bottom Gloucester City, but this was a fourth game without defeat and they are definitely giving themselves a chance of a miraculous recovery from what looked likely to be certain relegation a few weeks ago.
Kodi Lyons-Foster gave the Hawks a 20th minute lead that Aaron Lamont cancelled out 5 minutes later.
The White Tigers led at the break, thanks to Tyler Harvey`s 37th minute effort.
But just 5 minutes after the restart, a Ben Harding own goal restored parity and Goldy Omotayo won it for the home side in the 64th minute.
The Hawks would also have been boosted by the news that second-bottom Bognor Regis Town and third-bottom Poole Town were also beaten on Saturday.
Bognor suffered a 3-0 home defeat to mid-table Wealdstone at Nyewood Lane.
A Tommy Scutt own goal set the Stones away after 39 minutes and then new signing Ian Gayle doubled the visitors lead on 64 minutes.
But just two minutes later, Wealdstone went down to ten-men when Ricky Wellard was penalised for shirt pulling and dismissed as it was his second booking.
A third goal for Abobaker Eisa 8 minutes later though settled the points.
Poole lost by the odd goal in five at Tatnam against a Welling United side who are now just four points off a top seven spot.
Harvey Willard gave the Wings a great start with a goal inside 4 minutes.
Marvin Brooks equalised 7 minutes later and the Dolphins led at the break, thanks to a 16th minute Warren Bentley effort.
But a brace from Bradley Goldberg in the 57th and 65th minutes sealed three points for the visitors.
St Albans City are eighth after being held to a 1-1 draw at Priory Lane by mid-table Eastbourne Borough.
Kane Wills gave Boro a great start with a goal inside 2 minutes.
Rhys Murrell-Williamson eventually pulled the Saints back on terms.
A minute from the end of normal time, Boro`s James Haran received a second yellow card for an alleged head-butt on Harvey Bradbury, who swiftly follows him for an early shower, also with a second booking.
Bath City eased past in-form Concord Rangers to win 2-0 at Twerton Park.
The Beachboys came into the game as one of the form teams in the division, having gone thirteen games without defeat.
But Bath ahead just before half-time through Jack Batten`s header.
And then Jack Compton doubled their advantage 10 minutes from time with a stunning second.
East Thurrock United secured a much-needed win against struggling Oxford City.
Calvin Ekpiteta opened the scoring from close range after 13 minutes.
Four minutes later Ekpiteta fired past `keeper Craig King to double the Rocks lead.
Matt Paterson sent a fine curling strike beyond Lukas Lidakevicius to reduce the deficit after 64 minutes.
And the Rocks went on to net two late goals in the 86th and 88th minutes, courtesy of Sam Higgins` free-kick and Montel Agyemang respectively.