It was the first of four games in hand Gary Peters' side have over some of their rivals, but they failed to take full advantage.
However, they did manage to keep up an impressive unbeaten record in the league which stretches back to Boxing Day.
The home side had the better of what was an open and entertaining first half, even though it produced no goals.
Liam Hatch latched onto a long ball from Joe Devera after ten minutes, but smashed over from a tight angle.
The big striker also headed a Nicky Bailey cross over before the visitors had their first big chance of the evening.
They put together a neat passing move which ended with Ben Davies playing the ball into the dangerous Derek Asamoah, who turned and shot against the inside of the post.
However, Barnet showed their own touch of class through Jason Puncheon on the half-hour mark, when his left-foot screamer from 30 yards forced a wonder save out of Chris Mackenzie.
But the goalkeeper did not look as assured on the stroke of half-time when Adam Birchall rushed onto a long ball, looped it over him, but shot against the bar with an open goal gaping.
Barnet were clattering the Shrewsbury woodwork again ten minutes after the break, and this time it was Hatch who volleyed against the underside of the bar when the visitors failed to clear a corner.
But it was defender Ismail Yakubu who had arguably an even better chance to break the deadlock for the Bees on 61 minutes, but Mackenzie again produced a wonderful stop from his free header from a Bailey set-piece.
Barry Cogan also went close in the closing stages, but Barnet failed to take advantage of their dominance and even suffered a scare when Kelvin Langmead hit a post in injury time.