John Akinde has scored 15 goals in League Two this season
Plymouth's lead at the top of League Two was cut to three points after Barnet inflicted a second home defeat on the Pilgrims in four days.
The Bees went ahead when Bira Dembele was left unmarked from a corner, and scored with a looping header.
David Fox hit the bar from the edge of the box for Argyle, while Jake Jervis had a strong penalty appeal waved away.
The division's top scorer John Akinde doubled Barnet's advantage, beating the offside trap before slotting home.
Visiting keeper Jamie Stephens made two great saves to keep Plymouth out - from Jervis's shot and Sonny Bradley's powerful header.
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