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Nottinghamshire 168 for 6 (Clarke 42, Moores 47) beat Worcestershire 164 for 9 (Munro 66, Fletcher 5-32) by four wickets
Seamer Luke Fletcher took a career-best five for 32 as the Rapids were restricted to 164 for nine in their 20 overs, before Clarke hit 52 from 34 balls and Moores clubbed three sixes in his 31-ball assault before Calvin Harrison hit the winning boundary with just two balls to spare.
New Zealand big hitter Colin Munro, who spent the 2014 and 2015 seasons at New Road, began his third Blast campaign with the Rapids with 66 off 43 balls - his highest score in their colours.
Otherwise, it had looked like a below-par display by the visitors after being asked to bat first, with Ben Cox's 20 the next highest score, but with two wickets each from Brett D'Oliveira and Yorkshire loanee Matthew Waite the finish was closer than anticipated.
Fletcher's five-wicket haul came after his first three balls of the night had gone for four, six and six at the hands of Ed Pollock. Former England pace bowler Jake Ball, in his first match since last July after recovering from a stress fracture in the back, took two for 24 and skipper Dan Christian two for 22.
Worcestershire had 56 runs on the board from their powerplay but lost a third wicket to the last delivery when a slow bouncer from Ball deceived Jack Haynes, who shaped to cut and succeeded only in nicking a catch to 'keeper Moores. It meant that a dropped catch in the same over, when Haynes was put down at deep point, had cost only one run.
The other casualties were Pollock, who attacked Fletcher in characteristic style with four-six-six as the Outlaws stalwart struggled to get his length right, only to hit a low full-toss straight into the hands of Alex Hales at mid-on. D'Oliveira was caught behind off Dan Christian in an attempted scoop.
Rapids were 86 for three at halfway. Munro pulled six and cut for four off consecutive balls of Calvin Harrison's leg spin and after Jake Libby skied Christian to mid-off a lot seemed to rest on the shoulders of the Kiwi.
A big chance went begging when Moores missed a good stumping chance off Matt Carter when Munro was on 66, but in the event the error cost nothing as Munro top-edged a slow bouncer from Fletcher and was well caught at short third man, having hit seven fours and two sixes.
Cox pinged a six over midwicket in the same over but fell two balls later attempting the same shot as the innings ended badly for the Rapids, who lost five wickets in the last four overs while adding only 28 runs, with Fletcher picking up two more in the final over.
After the Outlaws lost Hales cheaply, Ben Duckett cleared the legside boundary twice in his 29 from 14 balls but after nonchalantly lofting the second of those sixes was caught at square leg attempting a repeat, rather throwing away the chance of a big score.
At 66 for 2 from the powerplay, Notts were ahead, although they lost Samit Patel for four and Clarke too might feel he should have had more, going after D'Oliveira's leg spin with fewer than 50 required in the 13th over and paying the price.
A bad drop by Haynes at long on off D'Oliveira let Moores escape on 28 and though Moores and Steven Mullaney holed out off Matthew Waite in the penultimate over as the home side threatened to wobble at the death, Harrison found the boundary off Charlie Morris to see them home.