Barlow made it three goals in two games since joining the club when he struck twice in the space of six minutes at the start of the second half. The former Everton man opening his account on 49 minutes when he rose unchallenged between two defenders to head in a cross from David Perkins.
Two minutes later Barlow struck again, racing through a gap in the home defence before producing a clinical finish.
Crawley gave themselves a lifeline 16 minutes from the end when Morecambe skipper Jim Bentley was adjudged to have pushed Chris Giles and Daryl Clare made no mistake from the spot to register his ninth goal of the season.
But Crawley's joy was short-lived two minutes later when Perkins raced through another big gap in the middle of the home defence and gave Smith no chance with his low finish.
Victory was no more than Morecambe deserve. They had been more of a threat in a terrible first half with big striker Wayne Curtis twice going close.
The arrival of the substitute Danny Ekoku and Neil Jenkins gave Crawley much needed impetus, but manager John Hollins knows his side will have to defend a lot better if they are to climb away from relegation trouble.
Morecambe's first win in six games means they are firmly back in the play-off race and Barlow already looks to be a very shrewd acquisition.