The visitors had Lee Noble sent off 10 minutes before the break after receiving two yellow cards inside five minutes.
Loick Pires was impeded by Adam Green and sub Sole scored from the spot.
VIEW FROM THE DRESSING ROOM
Woking manager Garry Hill told BBC Surrey:
"Dartford gave us a hard game and they showed there resilience like they did last season and they were going to try and prove a point.
"I think the big turning point in the game was the sending off and I think the player lost his head and they were two bookable offences and as I say to my players you have to keep your discipline in this league because the referee will deal with it.
"We had to be patient tonight and wait for the opportunity and that was the difference and I was pleased with the first three points."
Dartford manager Tony Burman told BBC Radio Kent:
"It's very cruel - but that's football. The guys worked very hard, especially when they went down to 10 men.
"Lee's lost it but he's been fouled twice and the referee is standing there and not given a foul. He's got to keep his composure in those situations but the referee got it wrong.
"Why does the referee have to go to his cards straight away? He's got it wrong.
"I think we more than matched them and I thought we caused them more problems. I cannot fault the effort and I'm proud of them tonight."
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