Barnet almost hit back immediately with Matt Lockwood running in on goal but shooting straight at Barry Roche, who saved smartly with his legs.
The Bees did pull one back after 33 minutes, Lockwood sending Roche the wrong way from the penalty spot after Danny Adams had been penalised for a shirt pull.
Phil Jevons hit the bar for Morecambe after the break, before playing Duffy through to make it 2-1 with 12 minutes remaining.
The Shrimps finished strongly and hit the woodwork on two further occasions late on.
Source: Team Talk
Source: Team Talk