The Reds had failed to score more than once in their previous 10 League Two games, but were dominant against Warren Feeney's side.
County striker Scott Boden opened the scoring at the wrong end when his header beat Joe Day after 36 minutes.
Shamir Fenelon then headed home eight minutes after the break, before Newport's Medy Elito was sent off with five minutes left for two yellow cards.
"It was disappointing, I don't think we got going from the first whistle, we couldn't get into a rhythm and our passing was poor," Newport manager Feeney told BBC Radio Wales.
"We have to put it to bed and move on to the next game, we are still in a fantastic position to avoid relegation and that is still my aim.
"You have ups and downs in a season and this was a down, the worst performance since I have been the manager. No-one likes to get beaten."
Crawley completed a double over Newport County with a comfortable 2-0 victory.