The visitors, who have won two of their first five games, were pegged back by tight bowling from Adil Rashid (3-23).
But Yorkshire never got going in reply, Herschelle Gibbs top-scoring with 19, while Anthony McGrath was left stranded on 18 not out.
Northants captain Andrew Halls told BBC Radio Northampton: "As we've said in the past - it only takes one win to spark the guys off.
"It's been really great. The team has rallied round beautifully and there's still plenty of motivation.
"They want to do well in this competition."
BBC Radio Northampton's Geoff Doyle: "After three defeats in a row that's two wins on the trot and the Steelbacks Twenty20 form appears to have returned.
"Yes they were helped by the weather but they had taken the wickets of the key batsman by then so they deserve their win.
"Special mention to Jack Brooks who made his county debut less than a year ago and before that was playing club cricket; his bowling matures by the game."
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