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."
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