A superb second-half performance saw Jim Harvey's side come back from a goal behind to clinch a deserved draw on a tense afternoon.
It was the introduction of young striker Danny Carlton after the break that changed the pattern of the game. His pace gave the Shrimps a new dimension and caused the tight Bees defence a number of problems.
The first half saw both sides struggle to gain control of the game with both defences very much on top until Barnet were gifted a lead out of the blue on 27 minutes.
A long clearance should have caused the Morecambe defence no problems but keeper Ryan Robinson hesitated along with central defender Darren Kempson and Liam Hatch nipped in between the two to head the ball into the empty net.
It was a rare attacking moment of a first half that failed to inspire, but the second half was a totally different affair.
Carlton gave the Shrimps a new edge and put Barnet under pressure for the first time. He was immediately in the action with a great chance on 46 minutes after Ismail Yakubu's slip but he curled his shot well wide.
Seconds later, keeper Shane Gore was forced to tip over Chris Blackburn's dangerous cross and Lee Elam broke through but missed his kick as he looked to square the ball to Michael Twiss.
Elam was not to be denied for long, however, as he fired his side back into the game on 57 minutes. Wayne Curtis was the architect with a great run at the heart of the Barnet defence before teeing up Elam whose shot beat Gore via a wicked deflection.
Three minutes later things looked even better for Morecambe as Gore was sent off for hauling down Carlton outside the box as he raced through.
First choice keeper Scott Tynan came on and was quickly in action with a great save from Curtis' free-kick before Simon King produced a brilliant last-gasp tackle to defy the lurking Twiss.
The Shrimps continued to press with Tynan saving smartly low to his left after an excellent run and shot from Twiss before Kempson headed a Carlton free-kick just wide.
The best chance of a winner, however, came for the visitors seven minutes from time. Substitute Patrick Ada crossed from the left for Lee Roach to side-foot wide from six yards out when he looked certain to score.