The 39-year-old, who will retire from first-class cricket at the end of the season, made 121 out of a total of 313-7.
Yorkshire came up short in their run chase as they closed on 289-9 to lose by 24 runs.
Sangakkara's 39th one-day hundred adds to his 61 in first-class matches, 38 of which came in Test matches for Sri Lanka.
In Tuesday's other last-eight tie, 834 runs were plundered in an extraordinary match as Nottinghamshire edged out Somerset by 24 runs in Taunton.
First Published: June 14, 2017, 9:57 AM IST