Cole Stockton added to his growing reputation as he scored a late goal to earn the Shrimps a battling point against Barnet.
The on-loan Tranmere striker scored with nine minutes to go as the Bees looked set to seal the points after two goals from John Akinde either side of a Tom Barkhuizen header put the home side in the driving seat.
Jim Bentley's side started well and Paul Mullin hit the post in the opening minutes of the game.
But, not for the first time this season, the Shrimps conceded an early goal as Barnet took the lead on seven minutes when Michael Nelson found Akinde in the area and the Bees' striker fired a right foot shot past Barry Roche from six yards out.
The Shrimps bounced back almost straight away and levelled just two minutes later when Barkhuizen headed past Jamie Stephens after the ball had come back off the post.
At this stage the Shrimps were playing some fine free-flowing football and the woodwork denied them again when Michael Rose smacked the post with a stunning effort and three minutes later the post came to Barnet's rescue for a third time through Stockton.
The Shrimps were not having it all their own way however and Kevin Ellison produced an excellent goal line clearance before Barnet regained the lead on 31 minutes when after a Rose mistake Akinde was in the right place at the right time again with another right footed shot from inside the area beating Roche.
Barnet started the second half well and Akinde remained a major threat only being denied a hat-trick when his close range header was well saved by Roche just before the hour.
The home side continued to press with Roche saving smartly again from Mauro Vilhete before the Shrimps ended the game strongly.
Substitute Jack Dunn fired over just moments after coming off the bench and with nine minutes to go Stockton scored his second goal in two games with a cool finish after being found by James Jennings.
Both sides went for the three points with the ever-dangerous Akinde drilling a shot wide at one end and Ryan Edwards forcing a save from Stephens in the 90th minute but in the end both had to settle for a point, the Shrimps' first draw of the season.
Barnet: Stephens, Johnson, N'Gala, Nelson, Vilhete, Weston, Togwell, Akpa Akpro (rep Gambin 87), Nicholls (rep Batt 83), Campbell-Ryce, Akinde. Subs not used: Vickers, Watson, Sesay, Taylor, Shomotun.
Morecambe: Roche, Wakefield, Edwards, Winnard, Jennings, Kenyon (rep Murphy 78), Rose, Barkhuizen (rep Molyneux 68), Mullin (rep Dunn 66), Ellison, Stockton. Subs not used; Nizic, McGowan, Conlan, Massanka.
Ref: G Ward