Goals from Ben Tomlinson and Andrew Boyce helped Lincoln maintain their good start with a win at Dartford.
Tomlinson put the Imps ahead from close range before home keeper Alan Julian denied Nathaniel Brown.
Boyce doubled the lead, finishing from 12 yards but Elliot Bradbrook's header then reduced the deficit.
Adam Birchall almost rescued a point for the hosts with four minutes remaining but his header was punched clear by visiting keeper Paul Farman.
VIEW FROM THE DRESSING ROOM
Dartford manager Tony Burman told BBC Radio Kent:
"It was two set-pieces. We switched off. We didn't play as well as we could have done and they've done a job on us, but second half I couldn't fault the guys.
"It was 100% handball - no question. Anywhere else on the pitch it's handball and that's the second Saturday in a row. It was on target and it was handball.
"The referee says it was handball but it wasn't intentional. It's absolute rubbish."
Lincoln City manager Gary Simpson told BBC Radio Lincolnshire:
"They put us under a bit of pressure at the end. They had nothing to lose so it was all hands to the pump, but we played some good football at times.
"We changed our shape a little to play through them and it paid off,. We were 2-0 up and playing some good stuff but the goal gave them impetus so we had to revert back to the formation we've had (in previous games) and soak it up. But we had chances to go further in front and it was end-to-end.
"As a team we've looked quite solid and we've got to keep working hard and keep doing that.
"In life you have to enjoy the good times and there's a long way to go. We've only played six games but I'm glad we're fourth from top rather than fourth from bottom."