Matt Tubbs grabbed both goals to lift Crawley up to second in League Two as Carl Fletcher lost for the first time as Plymouth's caretaker manager.
Tubbs steered in Kyle McFadzean's mis-hit shot and doubled the hosts' lead when he was left unmarked and fired home from inside the penalty area.
Tom Eastman, McFadzean, Tubbs, Tyrone Barnett and Sergio Torres all missed further chances for the dominant Reds.
The Pilgrims' best opportunity fell to Curtis Nelson but he headed just wide.
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Crawley manager Steve Evans told BBC Sussex:
"It's a great win for us. On another day if we had a bit more quality in the final third it could have been any score.
"We could have perhaps taken more advantage of attacking positions we got ourselves in. But you have days like that.
"Carl certainly gets a shift out of his players. They never stopped defending or stopped trying.
"But the real winners today are Plymouth Argyle. I heard from one of their directors that it looks like their takeover is happening. That's the bigger picture and is more important."
Plymouth caretaker manager Carl Fletcher told BBC Radio Devon:
"It's back down to Earth for us now isn't it?
"It was always going to be tough coming here, they're obviously a good side and well organised.
"I'm gutted for the lads, as they've given everything and worked their socks off."