Harry Moore made his professional debut and Luis Reece struck 96, but Derbyshire were unable to chase down a sizable target in the reduced-overs game against Worcestershire Rapids.
Ali plundered 88 off only 36 balls and dominated a fourth wicket stand of 119 from 56 with skipper Jake Libby who made 73.
The 25-year-old hit seven sixes and eight fours after Rob Jones made 53 as the Rapids surged to 254 for 5 in a game reduced to 30 overs a side by rain.
Luis Reece led Derbyshire’s pursuit with 96 off 64 balls but Pat Brown took 4 for 51 and Josh Baker 3 for 29 to seal victory with 29 balls to spare and keep the Rapids on course for the knock-out stages.
Derbyshire collapsed to 192 all out but it was still a memorable day for seamer Harry Moore who at 16 years and 114 days became the youngest player to represent the county.
The Rapids initially started slowly after Derbyshire elected to bowl and kept the visitors in check with disciplined seam bowling.
Sam Conners set the tone by opening with a maiden and the pressure accounted for both openers in the first four overs.
Ed Pollock was bowled pushing forward at Conners and when Gareth Roderick came down the pitch to Suranga Lakmal he edged a drive to slip.
Moore’s first bowl in senior cricket was impressive as the tall right-arm seamer conceded only eight from three overs which helped restrict the Rapids to 50 from the first 10.
The scoring rate increased against the spinners with Jones driving Alex Thomson over long off for the first six of the innings and Libby repeated the shot in the off-spnner’s next over which cost 17.
Jones reached his 50 from 45 balls but then pulled Luis Reece to long on which ended a stand of 95 off 80 balls.
But that only brought in Ali who went into overdrive from the start, sweeping Mark Watt for six and dispatching Moore for another two maximums when the youngster returned to the attack.
Ali powered to his 50 with three consecutive fours off Conners before driving Watt for two more sixes.
He was closing in on Worcestershire’s fastest-ever one- day hundred when he drove Conners to long off and Libby followed in the next over, a skied pull giving Moore his first wicket.
Ben Cox provided some late momentum with an unbeaten 22 off 11 balls to take his side past 250 but Derbyshire responded well to a challenging chase.
Reece cleared the ropes twice in Matthew Waite’s second over and with Harry Came also timing the ball well, Derbyshire motored along at eight an over before Pat Brown broke through.
Brown, who will be playing for Derbyshire next season, had Came caught at deep midwicket but Reece continued to tear into the bowling.
After flicking Brown over backward square for six to reach 50 from 33 balls, he drove him for over long on for another maximum before hoisting Dillon Pennington high over the midwicket boundary.
Tom Wood pulled Pennington to mid on but when Waite returned, Reece hit him for three fours as 17 came off the over.
But Waite showed character by having Wayne Madsen caught at deep point and the dangerous Haider Ali lbw off the first two balls of his next over.
Reece then fell to Brown as three wickets went down in five balls with Derbyshire losing their last eight wickets for 47 in seven overs.
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