The striker rose well at the far post to head a fine Michael Twiss cross past Nicky Eyre eight minutes into the second half to give the home fans a welcome boost.
It was only Morecambe's second home win of the season, but they will feel they did enough to earn the points against a young Diamonds side that have now gone five games without a win.
The first half saw Morecambe start well and produce some good early moments.
On three minutes Carlton volleyed a corner from Twiss over the bar from eight yards out, before Twiss himself tried his luck with a 25-yard drive that flew inches wide of the right-hand post.
On 10 minutes the home side could have done better when presented with a chance by visiting defender Paul Watson, but Carlton again missed the target with his effort after a neat David McNiven lay-off.
The Shrimps continued to push forward with David Perkins drilling a left-foot shot just wide of the left-hand post, before Paul Hart's side produced their first real opening of the game on 22 minutes when a neat volley from Marcus Kelly forced Steven Drench into a smart save low to his right.
Morecambe soon regained the advantage with the busy Carlton again threatening to break the deadlock when he beat the offside trap on 25 minutes but shot weakly at Eyre from the left-hand side of the box.
Morecambe were then almost gifted an opening goal by Diamonds defender Jon Ashton when he inadvertently sent a bullet header from Adam Yates' right-wing cross against his own crossbar 10 minutes from the break.
Three minutes later, the visitors produced their best moment of the game when Andrew Rigby worked some space on the right and produced a perfect cross for top scorer Simeon Jackson who somehow missed the ball altogether and the chance went begging.
The striker was almost made to pay immediately when the home side came close to scoring a bizarre opener. Wayne Hatswell's attempted clearance hit Yates and bounced back towards his own line but the ball bounced inches wide of the Diamonds goal.
Morecambe continued to push forward in the second half and Michael Howard forced Eyre into a neat block on 52 minutes.
A minute later Carlton struck to give his side a lead they probably deserved, although there was a hint of offside as both he and McNiven found themselves unmarked in the box.
Hart's team staged a spirited but ultimately disappointing fightback. On 59 minutes Dave Savage produced a shot from the edge of the area that was deflected for a corner and, from the resulting dead ball, Ashton headed just wide from eight yards out.
The introduction of substitute Tyrone Berry gave the visitors an added edge in attack but they still failed to penetrate a Morecambe defence that kept their second successive clean sheet.
Michael Rankine let fly with a 25-yard shot that was well over the bar, but that proved to be the only real threat in the final stages.
The Shrimps were able to celebrate a welcome win with boss Sammy McIlroy hoping his side can produce a similar spirited performance when they travel to Crawley on Saturday.
Diamonds face another tough test when they meet Stevenage on Friday, hoping to end a run of three successive defeats.