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.
Crawley Town 25 Shearer 05 McFadzean Booked 19 Griffiths 26 Eastman Booked 28 Davis 08 Torres 13 Hunt 15 Bulman 27 Drury (Davies - 73' ) 09 Tubbs (Doughty - 87' ) 23 Barnett (Akinde - 81' ) Substitutes 01 Kuipers 02 Davies 21 Doughty 17 Akinde 29 Pittman Plymouth 23 Cole 02 Berry Booked 05 King (Lecointe - 84' ) 06 Nelson 03 Williams 07 Daley 08 Walton Booked 13 Soukouna 20 Hourihane (Hitchcock - 65' ) 21 Atkinson Booked (Griffiths - 80' ) 11 Feeney Substitutes 01 Larrieu 15 Young 22 Griffiths 10 Hitchcock 27 Lecointe