Striker Izale McLeod netted his 20th goal of the season as Barnet overcame nine-man Crewe.
McLeod's opener came from the penalty spot, after he was brought down by Alex defender David Artell, who was sent off for the tackle.
Adam Dugdale was also given his marching orders just before half-time for a late challenge on Ricky Holmes.
Michael Hector's second-half strike from Holmes's cross secured Barnet's fourth consecutive victory.
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Barnet manager Lawrie Sanchez told BBC London 94.9:
"We are better away than we are at home.
"I am glad they had nine men because if they had 11 men I think the result would be slightly different.
"We should have done a lot better than we did.
"We were poor, we started poorly. We got away with it today. If the other team had 11 men the outcome would not have been the same."
Crewe manager Steve Davis told BBC Radio Stoke:
"Dave (Artell) has dived in. You may as well stay on your feet because the lad's still got a bit to do, so I've no complaints about that decision.
"We had to regroup and I still thought we were the better side. They still couldn't get the ball off 10 men, and then 'Duggy' (Adam Dugdale) does something absolutely ridiculous and loses his head.
"Had we kept 11 men on the pitch, I feel we would have won the game quite convincingly.
"Those two have, quite honestly, cost us the game today."