Bates fell for 49, top-edging a sweep in the 12th over at 91/2, which brought the classy Satterthwaite to the crease as the run rate dropped below nine for the first time.
Satterthwaite hit four boundaries in her first nine balls faced to get the rate rolling along with Martin.
Satterthwaite made a rollicking 36 off 18 balls before she fell with the White Ferns 143/3 in the 16th over.
Keeper/batsman Martin was soon out for a well-made 54 off 34 balls.
Tauranga's Anna Peterson opened the bowling with her off-spinners from the port end conceding just five runs and ending with 0-24 off four overs.
Windies opener Hayley Matthews hit 16 off pace bowler Lea Tahuhu's first over from the other end to make her intentions clear.
White Ferns bowlers Devine and Hayley Jensen tightened things up well.
Matthews was dropped twice off Jensen in the fifth over and she made the Kiwis pay before being well stumped by Martin off Leigh Kasperek for 53.
Taylor led the charge for victory with a fine innings, with excellent placement and some lusting hitting to and over the boundary.
But with the win looking likely she was unable to get on strike when it mattered most in the final over.
Player of the Match Martin says they knew the world champion Windies would be tough competition.
"They are a very strong side and they bat all the way down with a lot of flair, so it is really pleasing and I think it will be a tight series all the way through," she says.
"We had a target in mind that we thought we could defend and we surpassed that today. It was good to get the first win on the board and also for the girls to have a good go with bat and ball.
"I enjoyed batting on (Bay Oval). It comes on quite nicely and a few of them that got through the field surprised me and went for four which was good on the lungs. It is really good out here and you do get value for your shots."
Match two in the series starts at 7pm tomorrowat Bay Oval under lights with free entry for spectators.
White Ferns 167/6 (KJ Martin 54, SW Bates 49, AE Satterthwaite 36; DJS Dottin 2-23, HK Mathews 1-24) defeated Windies 159/6 (HK Matthews 53, SR Taylor 51 no; LM Kasperek 3-35, SFM Devine 2-27) by nine runs.
