The New Zealand wicket-keeper hit 106 off 65 balls, including 14 fours and three sixes, as the visitors chased down their target of 161 in 17 overs.
World Cup-winning England captain Heather Knight ably assisted at the other end, finishing 48 not out.
Lauren Winfield's 58 had helped the hosts post a respectable 160-7 at York.
The 27-year-old shared a 67-run second-wicket partnership with New Zealand all-rounder Sophie Devine (41) before the latter was bowled by Anya Shrubsole.
Two late boundaries from South African Sune Luus looked to have led the Diamonds to a challenging total.
However, Priest - who had managed just three runs in her first two Super League innings - scored a majestic and at times brutal hundred, ending the match with back-to-back boundaries.
On a rain-affected day at the Ageas Bowl, Surrey Stars maintained their unbeaten start to the competition after edging to a four-run victory over holders Southern Vipers on the Duckworth-Lewis-Stern method.
Hayley Matthews removed Surrey's England opener Tammy Beaumont for a duck, but South African pair Lizelle Lee (40) and Marizanne Kapp (42) took the visitors to 127-8 on a slow wicket.
The Vipers' reply was hampered by a regular loss of wickets, as Stars captain Nat Sciver trapped Arran Brindle lbw, ran out Georgia Adams and bowled Charlotte Edwards for a duck, all in the space of 10 balls.
New Zealand captain Suzie Bates, who scored the first Super League century in her previous innings, continued her fine form as she hit an unbeaten half-century.
However, with the match finely poised and Vipers 100-7 - needing 28 off 22 balls - the rain began to fall in Southampton, which ultimately inflicted a first defeat of the competition on the home side.
Australian all-rounder Ellyse Perry starred with bat and ball as Loughborough Lightning thumped Lancashire Thunder by 50 runs.
Perry hit her first notable innings in the tournament, with her unbeaten 78 off 57 balls including 10 fours and a huge maximum, as Lightning scraped to a par total of 140-7 in Liverpool.
Thunder's response began badly as Perry bowled Emma Lamb (2) and trapped England wicket-keeper Sarah Taylor (4) lbw to reduce the hosts to 14-2.
Beth Langston (3-14) struck twice in an over - trapping both Natasha Miles and Sophie Ecclestone in front - as Thunder were bowled out for just 90.
Rachel Priest's brilliant unbeaten century led Western Storm to a 10-wicket victory over Yorkshire Diamonds in the women's Super League.