Keith Hill's first competitive game at Oakwell ended in disappointment as Carlton's six-yard strike and a neat finish from Ellison on his Shrimps debut secured victory.
Ricardo Vaz Te was handed his first Barnsley start, and the former Bolton striker brought the first save of the night from Barry Roche with a 25-yard volley.
Jacob Butterfield forced a fine stop from Roche with a shot from distance before Morecambe hit back as Lewis Alessandra blazed over and Gary McDonald fired wide from 12 yards.
Vaz Te flashed a 25-yard effort wide, sent a header over the bar and brought a great save from Roche as the Tykes got back on top before the break.
But it was the League Two side who opened the scoring at the start of the second half.
A right-wing cross from Izak Reid was flicked on by Alessandra and Carlton converted from close range.
Barnsley's response came from Danny Haynes, but his close-range header cleared the bar.
Both sides made changes, with Vaz Te leaving the action to be replaced by David Perkins.
Perkins blazed over just before the Shrimps doubled their lead. Carlton was the provider on this occasion, crossing for Ellison to drill the ball into the top corner from 12 yards.
Butterfield tried his luck from distance but Roche was equal to his effort and Perkins had the last chance of the game but fired wide from the edge of the box.