Shrewsbury boss Gary Peters readily conceded afterwards that the better side had won and described his side's performance as poor, especially in the first half.
That was a fair assessment of things and he admitted to being 'desperately disappointed' with a below-par showing from the Gay Meadow side, who approached the game in buoyant mood following an impressive 3-0 home victory over near-neighbours Hereford, six days before.
The opening stages promised some good things to come with Ben Davies' fine throughball resulting in Michael Symes forcing a diving save from Barnet keeper Lee Harrison. Shrewsbury struggled to bring any real penetration to their forward play throughout the remainder of the first half while, despite some neat approach work, the visitors were unable to produce much in the way of a serious goal threat.
After the break Shrewsbury improved and Davies twice tested Harrison, once with a curling free-kick and also with a rising snap-shot that was palmed over after the Barnet defence had failed to clear a long throw into the penalty area. From the ensuing corner Andy Cooke flashed a header narrowly wide, but as time ticked away it appeared that both sides would be unable to find a breakthrough.
Midway through the second half Puncheon produced Barnet's best effort of the game when his low drive was safely gathered by Shrews goalkeeper Scott Shearer - but he was given absolutely no chance when Puncheon struck decisively with eight minutes remaining.
When the Shrewsbury defence failed to properly clear a free-kick, the ball dropped to Puncheon who, from 20 yards, smashed a volley into the top corner as Shearer could only grope at thin air.