Only one win their previous five League Two encounters became one in six as the home side were held to a 2-2 draw - but after 29 minutes defeat starred them in the face as two goals from John O'Flynn gave the visitors a commanding lead.
But within a minute of O'Flynn netting his second goal Grant Holt had reduced the deficit and by the 34th minute Shrewsbury were back on level terms when skipper Ben Davies crashed home one of his powerfully struck free-kicks.
At that point Paul Simpson's men looked a good bet to complete the comeback by going on to win the match - but despite dominating long periods of the second half, Shrewsbury were unable to make another breakthrough and ultimately were left frustrated.
After falling behind in 17 seconds at Accrington a week ago, Shrewsbury found themselves trailing by the fourth minute as Neal Bishop headed into the path of the unmarked O'Flynn who made no mistake from ten yards.
Unable to find any penetration in their forward play, things became worse for Shrewsbury when more slack defensive work was punished by O'Flynn in the 29th minute, as he side-stepped goalkeeper Glynn Garner before sliding the ball into an empty net.
Shrewsbury's response was swift and 60 seconds later Holt was on hand to score his tenth goal of the season, nodding in from close range after central defender Graham Coughlan had headed back into goalmouth.
In the 33rd minute Davies blasted home his eighth of the season with an unstoppable free-kick from the edge of the penalty area and at this point Shrewsbury were the likely winners.
They were, however, unable to build upon a bright start to the second half and although Barnet 'keeper Lee Harrison had to tip over another Davies free-kick, he was relatively untroubled until the 86th minute when a fine diving save was required to thwart Holt's curling shot.