It was only his fourth win over the Scotsman in 16 career meetings, and his first since a 4-2 win over the world number six in the PTC Grand final three years ago.
Two-times world championship finalist Carter - who has dropped to 31 in the rankings - made breaks of 101, 51, 98 and 51 against an opponent who struggled to find the level of consistency that helped him overcome Mark Williams 5-2 in the last 16.
It was a major disappointment for Higgins, who was appearing in his 100th ranking quarter-final.
Selby eases through in early World Open test as Williams thumps Stevens
Carter will face Thailand's world number 33 Thepchaiya Un-Nooh, who completed a 5-2 success against Scotland's Anthony McGill to reach the last four.
Un-Nooh had enjoyed wins over Alan McManus, world champion Mark Selby and Mark King to progress to this stage, and seems to be growing in confidence.
WATCH: Stunning pot from Thepchaiya Un-Nooh sets up victory
McGill ran in 80 in the opening frame, but knocks of 73 and 60 helped Un-Nooh move 3-1 clear.
A 60 from McGill was enough to reduce the deficit, but a run of 125 enabled Un-Nooh to move 4-2 clear, and he pinched the seventh frame on the black after McGill had broken down on 62 to continue to run to what could be a first ranking title.
In the later session, Neil Robertson saw off competition from David Gilbert - despite not looking his strongest - to beat him by five frames to two, booking himself a place in the semi-finals
Meanwhile, defending champion Shaun Murphy was knocked out of the competition by compatriot Joe Perry who came back from two-frame deficit to win the next five in a row and progress to the semi-finals.
Higgins ousts Williams to reach World Open quarter-finals
World champion Selby loses to Thepchaiya at World Open