Robertson was far from his usual assertive self and was guilty of unforced errors from start to finish, allowing Carter to move two frames clear at the mid-session interval. He never looked back.
The Englishman, runner-up at last season's World Championships, was unable to break higher than 46 in the entire contest but did not need big builds to capitalise on the Australian's tepid performance.
A brisk run to 90 from Robertson for 5-2 was the highest break of the semi-final, but the 2010 Crucible winner wasted further chances for 5-3 and Carter moved in for the kill to book a final against either Marco Fu or Barry Hawkins, who play on Saturday evening.
Robertson began fluidly enough with a smooth 42 break in the opening frame, but it would be his best snooker - at least until it was too late.
A fluked red put Carter in to move ahead with a knock of 44, before 'The Captain' came through two failed snooker escapes to clear to pink after the Australian took on a final yellow when he could have forced another re-take.
An extremely scrappy second frame finished in a similar manner to the first, as again Robertson wasted a chance towards the end with loose position on the final red to allow Carter another late clearance for a 2-0 lead.
The roles were reversed in the third, with Carter whiffing a long red opportunity to return to the table. But though Robertson claimed his first frame, he was bossed by the Englishman's separate runs to 32 and 46 which secured a 3-1 mid-session lead.
The 15-minute break was Robertson's chance to gather his thoughts and re-focus, but it was the same old story in frames five and six as Carter kept his breaks at moderate length and his safety play tighter than his opponent's to find himself one frame away from the final.
And though Robertson finally snapped into life with a sharp visit of 90 to snatch a quick one back, three separate chances to put some serious pressure on Carter at 5-3 went to waste and sent the world number five packing.