Two goals in the space of three minutes by Jack Holland and Josh Rees before half-time gave Bromley a commanding lead.
And only a minute into the second half their cause was aided as Kane Ferdinand was sent off for a rash tackle.
Bromley are now up to sixth after a third consecutive National League win.
"That's our third clean in a row too," said manager Smith. "The defence has been very solid. We let ourselves down a little bit in the second half but I can't ask for anymore from them to go another win on the spin after the tough game we had on Tuesday.
"We defend from the front and it proved today. Keeping that clean sheet is brilliant for us.
"It was a fantastic result but we can be better than that. Fair play to Woking they made it difficult, sitting third before the day. For us to get that convincing win against them was a big ask from our players."
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