The persistence of Cliff Akurang created Barnet's first opportunity when he robbed David Artell near the touchline and his astute cut-back found the onrushing Albert Adomah, but the unmarked midfielder scuffed his shot wide.
Morecambe's direct approach nearly reaped rewards in the tenth minute when their giant-sized captain Jim Bentley trundled forward and met Stewart Drummond's cross with a header that crept just wide.
The visitors continued to grow in confidence and inched their way into the contest with Carl Baker and Drummond both drawing plunging saves from Barnet goalkeeper Lee Harrison.
The Bees' 4-5-1 formation prevented Jason Puncheon from having a telling impact in the final third and his frustration became apparent when he skied a 25-yard free-kick harmlessly over shortly before half-time.
Puncheon went desperately close four minutes after the restart when Josh Wright's free-kick fell invitingly for him, but his left-footed shot struck the base of the post with Shwan Jalal beaten.
Jalal then made a smart tip-over from Wright's long-range dipping effort.
Those missed chances proved costly as Morecambe took the lead on the hour mark when Garry Thompson thundered home Baker's corner at the second attempt.
Morecambe survived a late penalty scare but clung on for a win that their organisation merited.