Sammy McIlroy's side, playing their first ever game in the Football League, showed that they mean business in League 2 with a good, solid performance against Barnet.
The Shrimps defended superbly with skipper Jim Bentley and defensive partner David Artell outstanding and keeper Joe Lewis, on loan from Norwich, producing a world-class save at the death to deny Anthony Thomas.
In a game which kicked off 15 minutes late because of crowd congestion McIlroy saw his side start brightly with Michael Twiss firing straight at visitor's keeper Lee Harrison on three minutes when he really should have done better.
Harrison was then forced to save from an Artell header before the Bees found their feet.
Adam Birchall forced Lewis into an excellent save on 21 minutes, and Sagi Burton headed an Ashley Carew cross over from close-range as the half came to a close.
The second half saw the action switch from end to end with Morecambe coming close to scoring when Garry Hunter's volley from a Twiss flick beat Harrison but drifted just over the bar.
The Bees hit back again as the game wore on with Michael Leary shooting wide from distance and Birchall unlucky to see a shot deflected wide of the left-hand post.
Paul Fairclough's side thought they had taken the points on 84 minutes when Anthony Thomas curled a shot that was heading for the top right-hand corner until keeper Lewis produced that stunning world-class save to tip the ball onto the crossbar to ensure parity.
It was a result that delighted Shrimps' boss Sammy McIlroy. "It was great to get off the mark so early in the season,'' he said.
"It was a magnificent day for the club and for the fans and I think we did enough to earn a point. We had a great early chance for Michael Twiss but Barnet had a few chances as well and Joe Lewis produced a world class save at the death.''