The teams drew 3-3 at Farlington before holders Cosmos progressed with a 7-6 shoot-out success.
Phil Archbold, Carl Kirby and Jonathan Saunders were on target for Cosmos.
Cosmos currently top the MV Veterans League, having won five and lost one of their six games to date.
Their sole defeat was a 4-2 setback against Paulsgrove, helped by a Jake Daniels hat-trick.
Grove have won all four of their league fixtures so far.
Cosmos last season completed a trophy treble - winning the Meon Valley League and Cup and the Portsmouth & District Cup.
AFC Portchester Vets take on Meonstoke Vets in the other semi-final.
1. North End Vets green) v Paulsgrove
North End Vets green) v Paulsgrove. Picture: Keith Woodland Photo: Keith Woodland
2. North End Vets green) v Paulsgrove
North End Vets green) v Paulsgrove. Picture: Keith Woodland Photo: -
3. North End Vets' Phil Archbold, left
North End Vets' Phil Archbold, left. Picture: Keith Woodland Photo: Keith Woodland
4. North End Vets green) v Paulsgrove
North End Vets green) v Paulsgrove. Picture: Keith Woodland Photo: -