The 27-year-old striker rejoined Morecambe last month after being released by Bury and made the most of some poor set-piece defending to score twice in 10 first-half minutes after Mark Byrne had given the home side the lead.
Loan signing Sam Deering's cross was only half cleared by Chris McCready and Byrne duly turned in his fifth goal of the season after 20 minutes.
But Barnet's inability to deal with a Stewart Drummond free-kick cost them as Carlton stole in at the back post to nod home.
And with three minutes to go before half-time Carlton scored his second, knocking in from close range as the Bees again failed to deal with a Drummond delivery.
James Spencer should have put the visitors out of sight early in the second half before Morecambe goalkeeper Joe Anyon produced a great save to deny Charlie Taylor a late equaliser.
Source: PA
Source: PA