The Bears had won their previous four matches at the ground in this format.
But they were always struggling after the hosts posted 296-8 in 50 overs, as Steven Croft (67) and Martin Guptill (50) also made half-centuries.
Despite 73 from visiting captain Ian Bell and Jonathan Trott's 66, the Bears closed on 254-9 to lose by 42 runs.
Bell and Trott put on 89 for the third wicket, but England one-day international left-arm spinner Stephen Parry then put the squeeze on with an excellent 3-43 from 10 overs.
Buttler's highest score for Lancashire in both forms of limited-overs cricket actually came on what was his List A debut for the county since signing from Somerset ahead of the 2014 season.
This was the England man's fourth innings since returning from Indian Premier League duty.
Lancashire spinner Stephen Parry told BBC Radio Manchester:
"We haven't started too well in the T20s, so it was nice to start a fresh competition with a win. We haven't started with a win in the last few years in this, so hopefully we can build on this and get to a quarter-final.
"Warwickshire are a really strong side, as good a one-day side as we've played against in a while, with two quality players in Bell and Trott, so it was a great performance.
"When you get near to 300 in this competition, you've always got a chance. But, once we managed to break that partnership, we really squeezed and got the rate up."
Warwickshire captain Ian Bell told BBC WM:
"It was an outstanding toss to win. We definitely wanted to bat first. But Jos Buttler was the difference between the two sides in the way he played.
"He showed the options you need to turn a par score into one above par. Without him, they'd have probably only got 260, which we would have been very confident in chasing.
"To all our young players watching that, they can learn a lot from the shots he used, the angles he created and the calmness he had."
Jos Buttler hit a brilliant 91 off 73 balls as Lancashire made a winning start to their One-Day Cup campaign against Warwickshire at Old Trafford.