The Diamonds made the perfect start to this summer’s campaign, posting 162 for four and comfortably defending it as the Thunder responded with 134 for seven.
Alice Davidson-Richards enjoyed an excellent day with a brisk 22 at the death and then three for 20 from four overs of medium pace.
Home captain Lauren Winfield, who lost the toss, top-scored with 44 off 43 balls and shared 72 in 11.3 overs for the first wicket with Sri Lanka’s Chamari Atapattu (41).
But it was another England World Cup winner in Katherine Brunt who really boosted the total with a damaging 31.
She hit sixes straight and over long-on in a 16-ball assault, sharing 52 in just 4.1 overs for the fourth wicket with Davidson-Richards after the score had fallen to 100 for three at the end of the 15th.
Lancashire were missing England pair Kate Cross through injury and Sarah Taylor due to a family wedding, and the visitors dropped three catches, including Winfield on six and Brunt on two.
Brunt and England Academy’s Davidson-Richards hit the lion’s share of 74 off the last six overs.
Davidson-Richards then struck in each of her first three overs to squeeze Lancashire’s chase. Her first two wickets helped leave them 71 for three in the 12th over.
She bowled Eve Jones with her first ball in the 10th over and had Jess Jonassen caught at deep cover with her ninth ball.
When leg-spinner Katie Levick picked up her second wicket, that of dangerous New Zealander Amy Satterthwaite caught at long-on in the 13th for 28, Yorkshire had the game all but wrapped up at 78 for four.
Levick had made the initial breakthrough to get Emma Lamb caught at backward point, and later bowled Thunder captain Danielle Hazell to finish with three for 30.
Davidson-Richards then Natalie Brown stumped as Lancashire fell to 97 for six. They could not recover.
Both these two sides play Surrey Stars in their next match - Yorkshire at the Oval on Sunday evening and Lancashire at Emirates Old Trafford on Wednesday afternoon.