Jamie White scored the only goal as Salisbury inflicted an 11th defeat in the last 12 games on 10-man Dartford.
Striker White fired past Darts goalkeeper Alan Julian with a low left-footed shot from 12 yards after good work down the left from Elliott Frear.
Frear wasted a good chance to double the lead when he shot over from the edge of the box.
The visitors were then reduced to 10 men after Danny Harris got his second yellow card 15 minutes from time.
VIEW FROM THE DRESSING ROOM
Salisbury City manager Mikey Harris told BBC Wiltshire:
"It wasn't our greatest performance of the season by any stretch of the imagination.
"Dartford are in a relegation battle, it was a scrap and we came out on top. We managed to match their spirit.
"It's a results business. I'll take a clean sheet and a 1-0 win all day.
"We're evolving as a team, we've shown we can win games in different ways."
Salisbury City 01 Puddy 12 Kamdjo 03 Hart Booked 05 Clarke 16 Dutton Booked 06 Wilson 14 Sinclair (McPhee - 32' ) 11 Frear 09 White (Fitchett - 66' ) 10 Lewis 17 Feeney (Sinclair - 79' ) Substitutes 25 Bittner 13 Sinclair 07 McPhee 20 Fitchett 04 Brett Dartford 01 Julian 04 Sterling 14 Mitchell-King 38 McAuley 20 Burns 30 Woodyard (Collier - 60' ) 31 Stevenson 10 Bradbrook 17 Martin (Kamara - 69' Booked ) 11 Harris Dismissed after an earlier booking 39 Pugh Substitutes 24 Wellham 06 Cornhill 36 Kamara 02 Hill 15 Collier
Ref: Brett Huxtable