Barnet hit the woodwork twice as Plymouth held on for a point that kept them above the relegation zone.
Clovis Kamdjo hit the post with a fierce 18-yard strike for the visitors, before the defender came close with a flicked header on goal.
Alex MacDonald spurned the home team's best chance, latching onto a poor backpass but shooting wide.
Barnet nearly won it in spectacular style when Jordan Obita smashed a 35-yard free-kick against the bar.
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Plymouth Argyle manager Carl Fletcher told BBC Radio Devon:
"We knew it was going to be tough. They've got some good players and it was going to be a very tough game for us in tough conditions.
"It was a real battle and I think the lads applied themselves really well and worked hard.
"Unfortunately today we couldn't find a goal that could have got us the three points, but it just didn't happen for us."