Colin Larkin helped himself to a first-half hat-trick to confine Dartford to their third consecutive defeat and give Lincoln their fourth win in five.
Dan Gray opened the scoring for the Imps with a close-range header before Larkin's quick-fire treble.
His first, a close-range header, doubled the visitors' lead before he slotted home twice from inside the box.
Darts' Harry Crawford then fired in twice, from 25 yards and the edge of the area, but Lincoln held on to win.
VIEW FROM THE DRESSING ROOM
Dartford manager Tony Burman told BBC Radio Kent:
"You're shell shocked when that (going 4-0 down) happens, but it was three set pieces and a goal we should have done better.
"We haven't been terrible, we've not been torn apart. We got bullied in the set pieces and paid the price.
"If you go 3-0 down the belief starts to go. They hadn't done much wrong other than picking up people at set pieces."
Lincoln City manager David Holdsworth told BBC Radio Lincolnshire:
"That was very satisfying, a fantastic performance from the boys. To come here and get a victory like that takes a lot of doing. You have to lay down the gauntlet and roll up your sleeves and get stuck in and I felt we did that.
"We did the basics right. We put the ball in the right areas. Colin and Vadaine [Oliver] matched up brilliantly and we were strong defensively. Colin got the service and his experience showed.
"Dartford are a very good side and Tony's substitutions worked so we had to make sure we were on our game and we played very well.
"It's a big week ahead for us and we have to be focused. I can sense it and that's why it was such a good performance, we've stuck together. We won't get too high or too low, but we will enjoy it."
Live Text Commentary
Full Time The referee blows his whistle to end the game.90:00 +4:11
Lee Noble takes a inswinging corner from the right by-line to the near post.90:00 +3:52
Lee Noble takes a shot. Save by David Preece.90:00 +2:23
Elliot Bradbrook is ruled offside. Indirect free kick taken by David Preece.90:00 +1:59
Paul Robson gives away a free kick for an unfair challenge on Lee Noble. Free kick taken by Lee Noble.89:57
Ryan Hayes crosses the ball, save made by David Preece.89:14
The offside flag is raised against Vadaine Oliver. Indirect free kick taken by Tom Champion.87:10 Booking
Booking Mamadou Fofana is given a yellow card.86:56
Free kick awarded for an unfair challenge on Jacob Erskine by Tom Miller. Richard Rose takes the free kick.85:45
Free kick awarded for an unfair challenge on Vadaine Oliver by Elliot Bradbrook. Gary Mills takes the free kick.85:04
Elliot Bradbrook crosses the ball.83:51
Free kick awarded for a foul by Vadaine Oliver on Jon Wallis. Direct free kick taken by Elliot Bradbrook.83:22
Conner Robinson takes a shot. Marcus Bettinelli makes a save.82:13
Ryan Hayes takes a shot. Save made by David Preece.80:38 Booking
Booking Booking for Nicky Nicolau for dissent.80:25
The offside flag is raised against Vadaine Oliver. Marcus Bettinelli takes the indirect free kick.78:54
Lee Noble crosses the ball.76:24
Foul by Richard Rose on Conner Robinson, free kick awarded. Nicky Nicolau takes the free kick.74:38 Substitution
Substitution Adam Smith goes off and Conner Robinson comes on.73:08 Substitution
Substitution Jon Wallis on for Semi Ajayi.
Tom Champion produces a right-footed shot from outside the penalty box and misses right.72:26
The ball is sent over by Ryan Hayes, Gary Mills makes a clearance.70:48 Goal scored
Goal! - Harry Crawford - Dartford 2 - 4 Lincoln A goal is scored by Harry Crawford from inside the area to the bottom left corner of the goal. Dartford 2-4 Lincoln City.69:46 Booking
Booking Booking for Peter Gilbert for time wasting.67:16
Corner taken by Lee Noble, clearance by Vadaine Oliver.66:44
Vadaine Oliver concedes a free kick for a foul on Elliot Bradbrook. Direct free kick taken by Semi Ajayi.65:51
Outswinging corner taken left-footed by Nicky Nicolau from the left by-line, Tom Miller takes a shot. Save by Marcus Bettinelli.65:16
Corner taken by Nicky Nicolau.64:39
The official flags Vadaine Oliver offside. Free kick taken by Marcus Bettinelli.64:04
Ryan Hayes produces a cross, Jacob Erskine takes a shot. Save by David Preece.62:20
Centre by Ryan Hayes, Elliot Bradbrook takes a shot. Save made by David Preece.61:32
Corner taken by Nicky Nicolau from the right by-line, save by Marcus Bettinelli.60:58
Inswinging corner taken from the left by-line by Nicky Nicolau.60:29
Shot by Daniel Gray from just outside the area goes over the net.59:39
Tom Champion gives away a free kick for an unfair challenge on Nicky Nicolau. Direct free kick taken by Nicky Nicolau.56:51 Substitution
Substitution Ryan Hayes joins the action as a substitute, replacing James Rogers.56:51
Foul by Nicky Nicolau on Lee Noble, free kick awarded. Lee Noble restarts play with the free kick.56:26
Unfair challenge on Harry Crawford by Gary Mills results in a free kick. Free kick taken by Elliot Bradbrook.53:27
The referee blows for offside. David Preece takes the indirect free kick.53:01
Vadaine Oliver is penalised for handball and concedes a free kick. Richard Rose takes the direct free kick.52:37
Foul by Lee Noble on Peter Gilbert, free kick awarded. Free kick taken by Tom Miller.51:56
James Rogers sends in a cross, Daniel Gray manages to make a clearance.50:08
Vadaine Oliver fouled by Tom Champion, the ref awards a free kick. Gary Mills restarts play with the free kick.48:41
The assist for the goal came from Jacob Erskine.48:41 Goal scored
Goal! - Harry Crawford - Dartford 1 - 4 Lincoln A goal is scored by Harry Crawford from outside the penalty area to the bottom right corner of the goal. Dartford 1-4 Lincoln City.46:26
Lee Noble takes a shot. Save made by David Preece.45:01
The referee starts the second half.45:01 Substitution
Substitution Jacob Erskine joins the action as a substitute, replacing Danny Harris.45:00 +2:40 Half time
Half Time The referee calls an end to the first half.45:00 +1:46 Goal scored
Goal! - Colin Larkin - Dartford 0 - 4 Lincoln Colin Larkin scores a goal from close range to the bottom left corner of the goal. Dartford 0-4 Lincoln City.45:00 +0:26
Strike on goal comes in from Gary Mills from the free kick, save by Marcus Bettinelli.45:00 +0:26 Booking
Booking Semi Ajayi receives a caution.45:00 +0:10
Free kick awarded for a foul by Semi Ajayi on Colin Larkin.42:36
Adam Smith is flagged offside by the assistant referee. Free kick taken by Marcus Bettinelli.41:57
Danny Harris gives away a free kick for an unfair challenge on Daniel Gray. Direct free kick taken by Daniel Gray.38:09 Booking
Booking Booking for Adam Smith.37:44
Shot from just outside the box by Nicky Nicolau goes over the crossbar.36:25
Corner taken left-footed by Nicky Nicolau from the left by-line, Colin Larkin produces a right-footed shot from inside the area that goes over the bar.35:56
Inswinging corner taken left-footed by Nicky Nicolau from the right by-line, Elliot Bradbrook makes a clearance.35:12
The official flags Harry Crawford offside. Tom Miller takes the indirect free kick.33:38
Unfair challenge on James Rogers by Mamadou Fofana results in a free kick. Lee Noble crosses the ball from the free kick right-footed from right channel, clearance by Tom Miller.31:24
Assist by Vadaine Oliver.31:24 Goal scored
Goal! - Colin Larkin - Dartford 0 - 3 Lincoln Colin Larkin grabs a goal from inside the six-yard box to the bottom right corner of the goal. Dartford 0-3 Lincoln City.31:24
Vadaine Oliver produces a cross,29:54
Nicky Nicolau decides to take a short corner.28:33
Lee Noble produces a right-footed shot from deep inside the area which goes wide of the left-hand post.26:17
The official flags Colin Larkin offside. Semi Ajayi restarts play with the free kick.23:12 Goal scored
Goal! - Colin Larkin - Dartford 0 - 2 Lincoln Colin Larkin scores a headed goal from inside the six-yard box. Dartford 0-2 Lincoln City.21:57
Outswinging corner taken by Nicky Nicolau from the left by-line played to the near post, Tom Champion manages to make a clearance.21:24
Corner taken left-footed by Nicky Nicolau from the left by-line, clearance made by Elliot Bradbrook.21:03
Tom Champion fouled by Vadaine Oliver, the ref awards a free kick. Tom Champion takes the direct free kick.19:31
Danny Harris fouled by Tom Miller, the ref awards a free kick. Lee Noble delivers the ball from the free kick right-footed from right channel, clearance by Gary Mills.18:55
The ball is swung over by Richard Rose, Effort from deep inside the area by Harry Crawford misses to the left of the goal.17:43
Harry Crawford is flagged offside by the assistant referee. Indirect free kick taken by Tom Miller.16:16
Foul by James Rogers on Paul Robson, free kick awarded. Direct free kick taken by David Preece.15:08
Peter Gilbert is caught offside. Marcus Bettinelli restarts play with the free kick.14:36
The ball is delivered by Richard Rose.13:05
Tom Champion takes a shot. David Preece makes a save.10:28
Free kick awarded for an unfair challenge on Danny Harris by Tom Miller. Shot on goal comes in from Lee Noble from the free kick.10:00
Adam Smith gives away a free kick for an unfair challenge on James Rogers. Direct free kick taken by Marcus Bettinelli.6:34
The assist for the goal came from Nicky Nicolau.6:34 Goal scored
Goal! - Daniel Gray - Dartford 0 - 1 Lincoln Daniel Gray finds the net with a headed goal from close in. Dartford 0-1 Lincoln City.5:58
Nicky Nicolau takes the inswinging corner,2:53
Unfair challenge on Tom Champion by Adam Smith results in a free kick. Direct free kick taken by Richard Rose.0:00
The referee gets the game underway.
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