Pembroke held their nerve in a tense chase to beat CSNI by three wickets in the quarter-final at Sydney Parade.
Chasing 207 they were rocked by three early wickets, including the Tucker brothers and Jack Balbirnie.
However they rebuilt with Theo Lawson and Dane Heverin (24) adding 65 in 14 overs.
Lawson put on a further 46 with Shaheen Khan, before being trapped by McCarter for a fine 62 off 73 balls which included nine boundaries.
When Barry McCarthy (3) was run out afterwards to make it 127 for 6, CSNI were probably favourites.
However Khan too found the boundary nine times as he top scored with 67, adding a valuable 69 with Ryan Hopkins to take his side to the brink of victory.
Although he fell with 11 needed, there was no late dramas as Hopkins (26*) steered his time past the winning post.
CSNI's innings was dominated by overseas player Andre Malan, who hit 9 fours and a six in his unbeaten 109, coming to the middle after just two balls, when James Kennedy was adjudged lbw off McCarthy (3-39).
Gary Wilson made just 6, while Graeme McCarter (23) and Corin Goodall (20) offerd support to Malan.
Pembroke join Phoenix in the semi-finals, and they will be joined by the winners of the Leinster/CIYMS and Waringstown/Instonians quarter-finals on Sunday.
The National Cup semi-finals draw will take place on Tuesday.