Worcestershire 183 for 7 (Kashif 69) beat Leicestershire 150 for 9 (Patel 42, Brown 3-25) by 33 runs
Kashif, the first product of the South Asian Cricket Association to sign a pro contract with a first-class county, again demonstrated his potential with a sparkling 69 as Worcestershire recovered from 30 for 3.
Leicestershire reached 70 for 1 in the 10th over and looked to have laid the foundations for a worthy pursuit of a 184 target.
It means the Rapids have won their opening three games while in contrast the Foxes have been beaten in their opening trio of fixtures.
Mir has ended his brief and successful spell at New Road and will return to playing league cricket for Colwyn Bay, but will be replaced by Mitchell Santner who flies in tomorrow after being part of the Chennai Super Kings IPL squad.
The Rapids got off to a shaky start after captain D'Oliveira opted to bat.
Bracewell lasted only three balls before he was trapped lbw by a full-length ball from Naseem Shah when working to leg.
D'Oliveira took a stride down the wicket in the next over from Wiaan Mulder and only succeeded in nicking through to keeper Harry Swindells
Jack Haynes immediately went on the offensive with four boundaries in Shah's second over before was lbw deep in his crease to Mulder.
Kashif mixed some wristy strokes with sheer power as he and in-form Adam Hose set about rebuilding the innings.
They added 45 when Hose, who had top-scored in the wins over Northamptonshire Steelbacks and Yorkshire Vikings, tried to slice Callum Parkinson over the off side and fell to Colin Ackermann's catch running back from cover.
A pull for six and a delightful cut to the ropes in the same over from Reehan Ahmed enabled Kashif to complete a 33-ball half century.
Shah's return to the attack brought about Kashif's downfall when he found the hands of deep backward square.
In the same over, Ed Pollock was run out first ball by Ackermann's direct hit from mid on.
But Mir profited from being dropped being he had scored to plunder an unbeaten 32 from 15 balls and Ben Cox struck a typically breezy 28 as Worcestershire recovered from their early troubles.
When Leicestershire batted, Bracewell struck an early blow when Sol Budinger clubbed a delivery straight to Hose at deep mid wicket.
But Nick Welch scored freely and crucially Leicestershire kept wickets in hand, losing only one in the powerplay.
D'Oliveira brought himself into the attack and made a double breakthrough in the space of four balls.
Welch was pouched at long on by Haynes and Ackermann was bowled via an inside edge and his pad.
Rishi Patel hurried to 42 but, having hit the previous two deliveries from Mir for four, he gave his wicket away when charging down the pitch and being stumped.
The Pakistan leg-spinner's final over of his current spell at New Road also yielded a wicket when Arron Lilley was leg before aiming a blow over mid wicket.
Mulder and Rehan Ahmed fell cheaply to end Leicestershire's last hopes and then Pat Brown wrapped up the tail as he showed more encouraging signs of returning to his best form.