Boldewijn’s late brace condemned bottom-of-the-table Barnet to their fifth consecutive Sky Bet League Two defeat.
Crawley top-scorer Jordan Roberts threatened in only the fourth minute when he shot just wide of goalkeeper Craig Ross’ left-hand post.
Winger Jamal Campbell-Ryce should have hit the target for Barnet 12 minutes later when, from a Shaquile Coulthirst free-kick, he wastefully put the ball over from seven yards.
Crawley keeper Glenn Morris made a smothering save to deny ex-Reds striker John Akinde before Lewis Young headed over a good chance for the hosts.
Morris came to Crawley’s rescue again by diving to his right to save a 25-yard shot from Jack Taylor.
Crawley ended the half on the attack and midfielder Mark Randall should have worked keeper Ross when he blazed over from a Young pass.
Akinde had a right-footed shot saved shortly after the break before Young was denied at the other end from Roberts’ pass.
Crawley broke the deadlock in the 76th minute when from a flicked header by Roberts, Dutchman Boldewijn cut inside and planted the ball beyond Ross.
Boldewijn made the points safe three minutes from time by calmly stroking the ball home from a pass by Young for his fifth goal in four games.