Forward Bruno Andrade netted from the penalty spot before Shaun Jeffers added another on the stroke of half-time.
The match was streamed live on the BBC Sport website and Andrade displayed his talents again in the second half, getting his second and Boreham's third.
Zane Banton did get one back for the home side but it was a professional display from Wood in the opinion of manager Luke Garrard. He said: "We've done a job. I don't think we played to the levels we've set this season but you've got to give credit to St Albans, they had a go.
"I thought we could have exploited them a bit than we did but it's a cup tie. The underdog gets more of an incentive. We're in the hat on Monday which was the only aim.
"It's a derby, our support was fantastic. To allow them to go home or to a local pub and have the bragging rights is superb.
"There's more to come from Bruno. I feel like he's one of the better ones in the league. He's scored a brace and I think that was at half canter."
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