An ever changing experience saw the pair level at 2-2 at the mid-meeting stretch, with both Allen and Carter battling to track down their musicality.
It was all square after six edges, however Allen at last settled and ran through three in succession to seal the achievement.
I wasn’t on it this evening by any means, my timing was dreadful. I thought Ali played better compared to me,” Allen told ITV4.
Allen will confront either China’s Zhang Anda or Britain’s Imprint Selby in Sunday’s conclusive.
In the event that you think it seemed to be difficult work, it felt a ton more regrettable,” Northern Ireland’s Allen added.
I’m not content with how I felt and how I worked out there, yet everything revolves around results and I’m in the last.
Prior on Friday, Zhang held his nerve to beat previous world number one John Higgins 6-4.
Scotland’s Higgins won a crude opening casing yet lost the accompanying five as China’s Zhang ordered breaks of 102, 79, 84, 104 and 95.
Higgins, who won the opposition in 2021, showed strength to drive his direction once again into the conflict, winning three progressive edges to slice the deficiency to one, however Zhang found his stream again when it made a difference to secure triumph.