Kevin O'Brien made 75 and Simi Singh 70 not out as Leinster scored 286 off 49.2 overs, with Craig Young taking 4-50.
North West were all out for 181 off 44.2 overs in reply, Sri Lankan Irosh Samaraasooriya top-scoring with 77.
Ricki-Lee Dougherty contributed 42, while Ireland international George Dockrell ended with figures of 3-37.
Leinster are attempting to make it a treble of clean sweeps in the interprovincial tournaments this season and this victory gives them the start they had hoped for in the Inter-Pro Cup.
They will face North West Warriors again in a Twenty20 fixture at Bready on 26 May, with Munster Reds facing Northern Knights on the same date.
Ireland's Interprovincial Championship, plus their Twenty20 and 50-over formats were granted first-class status by the ICC in October.
It was the first time a domestic competition had been given first-class status outside a Test-playing country.
Monday's NCU Twenty20 results
North Down v Waringstown
North Down 146-6  R Pretorius 60
Waringstown 149-3 (17.2 overs) J Hall 47
Waringstown won by seven wickets
Carrickfergus v CIYMS
Carrickfergus 154 R Eagleson 30 no
CIYMS 156-1 (19.2 overs) C Dougherty 83
CIYMS won by nine wickets
Leinster Lightning began the defence of their interprovincial titles by beating North West Warriors by 105 runs in a 50-over match at The Hills on Monday.