Yorkshire 233 for 6 (Willey 118) beat Worcestershire 196 for 7 (Whiteley 65, Clarke 51) by 37 runs
Willey sent records tumbling with a 55-ball assault as the Vikings, invited to bat, posted a county-best 233 for 6 from their 20 overs. Fellow left-hander Whiteley then hit novice left-arm spinner Karl Carver over the ropes six times in the 16th over, which included a wide.
That took the score to 173 for 4, but he fell for 65 off 26 balls as the Rapids finished on 196 for 7, a 37-run defeat.
Sheffield-born Whiteley becomes the sixth man to hit achieve the feat in world cricket, including Lancashire's Jordan Clark, who did it in a second-team game against Yorkshire in 2013.
Whiteley said: "It was the right time in the game for me to go for it. It was all or nothing. Unfortunately for the bowler it was a short boundary on the leg-side.
"I had the mentality that I was going to go for it before I got in. I hit the first out of the screws and needed to keep going for the team, not for that achievement. It's something I never really thought I'd do in professional cricket.
"Personal milestone are great, but it's hard to get away from the defeat. It's pretty tough to take. We've lost four out of five and are right down at the bottom. Obviously we have to bounce back. There's no reason why we can't."
Yorkshire's coach Andrew Gale had only sympathy for Carver, even criticising his captain - and brother-in-law - Tim Bresnan for bringing him on to bowl.
"I blame poor captaincy for that," he said. "He shouldn't have bowled him at that part of the game. I felt for Karl, he's got a good record in T20 cricket and he'll bounce back. Ross nearly did it a few years back against us. It was good striking."
England limited-overs all-rounder Willey hit nine fours and eight sixes, helping to take 34 off John Hastings in the 17th over as he reached his second ton off 49 balls.
It was Yorkshire's record individual score and the highest in the Blast this season. It was also the highest by any team this season and their record score, beating 227 for 5 against Notts earlier this month.
Yorkshire flew out of the blocks and rarely broke stride in an innings which was only briefly interrupted by rain.
Alex Lees, in for ineligible former Worcester man Tom Kohler-Cadmore, hit an early straight six off Hastings onto the Football Stand roof before being bowled two balls later.
Willey and Adam Lyth, whose 31 off 23 balls was Yorkshire's next best score, then shared 81 in 6.2 overs for the second wicket before Willey and Jack Leaning later added 67 for the fifth wicket in 4.4 to advance from 148 for 4.
Willey, fresh off 70 in Friday's win over Birmingham here, fell in the 19th over when he was bowled trying to paddle Ed Barnard to third-man.
The Rapids kept pace with Yorkshire in a rain-affected chase and were even ahead of Duckworth Lewis Stern for much of the Powerplay as Australian all-rounder John Hastings was promoted to open, but they lost Ben Cox to Azeem Rafiq with the last ball of the sixth over to put them behind again at 60 for 2 and eventually slipped to their fourth defeat in five North Group matches.
Hastings hit Yorkshire captain Bresnan for two sixes and a four in the first over before falling in the third, caught at deep mid-wicket for 24.
Clarke continued the blitz but lost Ben Cox caught at cover off an Azeem Rafiq full toss shortly before a half-hour rain break.
They reached 102 for 2 after 10 overs before excellent Adil Rashid struck twice, including Clarke. Then came Whiteley, too late to affect the result, but entering the records in style all the same.