There were two changes to the starting line-up with Luke Foster and Tom Miller recalled at the expense of Jake Sheridan and Dan Gray. Foster started in a role just in front of the central defenders whilst Miller was a straight swap for Gray at right-back.
City kicked off and started brightly, putting the home defence on the back foot with Danny Rowe warming the palms of Alan Julian with a dipping, swerving effort from range four minutes in.
A corner to the Imps followed which was easily dealt with by the Dartford back line whilst at the other end Alex Woodyard blazed well over after the hosts' first corner fell to him 25 yards from goal.
A quiet spell ensued with play mainly in the middle third before Paul Farman was forced to palm away a low Danny Harris drive. City's response saw the overlapping Sean Newton win a corner on the left and when Rowe whipped in from the quadrant the ball fell to Foster who saw his powerful drive tipped on to the post by Julian. The ball ran kindly for the Imps though and there to fire home from close range was Ben Tomlinson for his third of the week.
The goal seemed to take the steam out of Dartford who promptly played a few misplaced passes, bringing some annoyance from the home fans in the sunshine behind the goal.
Referee Lee Swabey had words with Jon Nolan in the 28th minute after the midfielder kicked the ball away in frustration having been penalised for hand ball. A trip on Harris by Foster then gave the home side a free-kick in a dangerous position but Lee Noble's delivery bounced straight out for a goal-kick.
Newton forced a third corner in the 33rd minute and, as was the case 13 minutes earlier, this led to a City goal with Andrew Boyce following up after Julian had kept out his header to fire home from six yards.
Another corner a minute after the restart saw Julian get a push from Boyce and as the home side looked for a response, Tyrone Sterling headed a Noble free-kick well wide.
Some good build-up play by the Imps led to a free-kick three minutes before the break but Rowe's long-range effort came to nothing after Boyce was pulled up for a foul. Kenny Clark was then booked for a late challenge on Mo Fofana.
The half ended after one additional minute.
HT: Dartford 0 Imps 2
There were no changes at the break so it was as you were as Dartford restarted the game.
The first action of the second period saw Nolan booked for dissent after Rowe conceded a throw-in on the left flank before Ryan Hayes replaced James Rogers for the Darts.
Harris tested Farman with a low skidding effort 10 minutes after the restart but the home side continued to press and when Burns whipped in a cross four minutes later, in nipped skipper Elliot Bradbrook to plant a firm header past Farman to halve the arrears.
Jake Sheridan for Waide Fairhurst was the Imps' first change of the game in the 64th minute and he was quickly in the action, setting up Fofana who dragged his effort wide of the target.
A quiet second half continued with Julian spilling a Miller free-kick before Max Cornhill replaced Noble for the home side. Shortly afterwards the Darts won a corner on their left but City stood firm as the heads went in with their response seeing Tomlinson head over from six yards out when the striker should have done better.
A second Dartford substitution saw Jason Prior replace Alex Woodyard before a Rowe chip forward was cleared for a corner as Tomlinson loitered. Boyce was penalised for a push, however, as he looked to meet Newton's inswinger.
Tomlinson was then inches away from reaching a Nolan ball over the top as 'keeper Julian sprinted off his line. Some good work by Sheridan saw him win a corner from the next foray forward as the clock ticked into the 85th minute.
The woodwork saved the Imps in the final minute when substitute Cornhill fizzed a low effort through a crowd of players whilst in the first of three added minutes home appeals for a penalty for hand ball after a ball crashed against Brown were laughed off by the referee.
A Dartford corner ended in a City free-kick before Bradbrook was cautioned for dissent and after the Imps dealt with another ball into the mix, referee Lee Swabey brought things to a close with another hard-working performance yielding another three points.
FT: Dartford 1 Imps 2