Adam Birchall brought Morecambe goalkeeper Barry Roche into the action with just two minutes on the clock when his near-post effort from the returning Nicky Nicolau's cross produced a sharp save.
Stewart Drummond then flashed a header just past the far post as the visitors began to look threatening before an intricate passing move resulted in Diarmuid O'Carroll back-heeling the ball into the path of Garry Hunter who dragged his shot wide of the far post.
In what was proving to be a lively opening, the Bees took the lead in the 18th minute through a fantastic solo effort from Albert Adomah.
Birchall played the ball to the flying winger who effortlessly beat full-back Andrew Parrish before unleashing a thunderous shot that gave Roche no chance.
In search of a second goal, the Bees saw Neal Bishop's 20-yard free-kick superbly turned away by Roche before, from Nicolau's corner, Cliff Akurang's header was cleared off the line by Hunter.
However, the home support were left dumbfounded three minutes before the break when Morecambe drew level.
Hunter saw his intended pass into the path of O'Carroll loop off a defender, but the forward showed great composure as his neat turn was finished off with a stunning shot that gave Lee Harrison in the home goal no chance.
The second half saw fewer chances created with both sides trying their luck from long range.
Harrison dealt comfortably with a low drive from Wayne Curtis, while at the other end Barnet substitute Michael Leary flashed an effort wide after the visitors defence had failed to properly clear a cross from Luke Medley.
Barnet piled on the pressure at the end and in the final few minutes saw both substitute Medley and captain Ismail Yakubu have efforts cleared off the line as Morecambe held on for a point.