They will now meet Belfast High School at Muckamore on June 20.
The Belfast school's win at Foyle and Londonderry College was the most exciting of the tournament so far. "Inst" needed two runs off the last ball with nine wickets down and Rory McCurry secured their place in the final with a boundary.
Foyle had set the holders a challenging total of 211 for 5 in their 40 overs with Steven Clarke leading the way with 113.
"Inst's" hold on the cup was slipping when they slumped to 102 for 5 but Danny Graham with 62 and Craig Livingstone with 37 saw them on their way to another final.
Foyle and Londonderry College 211 for 5 (S Clarke 113, D Smith 38, D Murdock 25no, J Shannon 2-34). RBAI 214 for 9 (D Graham 62, C Livingstone 37, D Smith 2-34). RBAI won by 1 wk.
Belfast High School had already secured their place in the final with a convincing 9 wicket win over the RBAI second eleven.
