The all-rounder struck 75 with the bat as the home side posted 252 for four at Drayton Park.
Ineson then returned four for 14 with the ball as Aldershot II were skittled for 98 in reply.
The triumph left Railway fourth in the table – with two wins from their five fixtures so far this summer.
Skipper Sandy Newsham won the toss and had no hesitation in batting first at the sun-drenched Portsmouth ground.
And she watched with pride as her troops put their north Hampshire visitors to the sword.
Zoe Stride top-scored for Triangle with 82 not out.
And alongside Ineson, she found good support in Eleanor Ridley, Ruth Charles, Sian Stayce and Emma Church, who all reached double figures.
Teenage bowler Hannah Burnett was the pick of the Aldershot attack as she marked herself out as one to watch in the women’s game.
The visitors’ chase never got going as Nikki Barlow took one for 34 is her second match.
Stayce (two for 22) was also among the wickets, while Charles bowled tightly to concede only 26 runs from her seven overs.
Railway hammered home their advantage with a run out, while keeper Ellie Bloxham took a catch and Leah Lind pouched two more.
The Drayton Park outfit travel to struggling Ropley on Sunday.
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