Derbyshire 235 for 7 (Khawaja 104, Hughes 66) beat Unicorns 200 (Reece 59, Turner 4-54) by 35 runs
Australia's Usman Khawaja scored his maiden one-day century for Derbyshire as they recorded a Clydesdale Bank 40 double over the Unicorns with a 35-run victory at Chesterfield.
Khawaja made 104 from 109 balls and shared a century opening stand with Chesney Hughes who made 66 out of Derbyshire's 235 for 7.
Luis Reece led the chase with 59 from 63 balls but his dismissal in the 35th over ended the Unicorns' slim hopes and they were bowled out for 200, with Mark Turner taking four for 54.
Derbyshire's only previous victory in the competition was against the Unicorns in early May and Khawaja and Hughes put them in a strong position to repeat that success with an opening stand of 138 in 26 overs.
Not surprisingly after so much rain, the pitch was slow but both batsmen reeled off some handsome strokes on a rare day of sunshine and blue skies.
Hughes scattered spectators behind the long on boundary by driving Bradley Wadlan's slow left-arm spin for the first six of the innings and Khawaja matched his partner when he swept Luke Beaven over midwicket in the next over.
Khawaja's cover driving was a highlight of Derbyshire's innings and after reaching his fifty from 66 balls, he pulled a second six off Reece who put down a sharp return chance when Hughes was on 55.
Hughes sliced a drive to cover three overs later but Khawaja moved smoothly to his hundred before he was bowled trying to reverse sweep and that sparked off a collapse which saw six wickets fall in 25 balls.
Wayne Madsen miscued a drive, Dan Redfern failed to clear long on and Garry Park, playing against his younger brother Craig, went first ball when he chipped a catch to cover.
Jon Clare got off the mark with a six that flew into a row of portable toilets but Glen Querl struck twice in the final over as the Falcons fell well short of the total Khawaja and Hughes put them on course for.
But it was still a demanding target for a team that had not previously scored 200 in the CB40 this season although they got off to a flier as James Ord and Wadlan plundered 30 from Turner's opening three overs.
Ord unleashed one of the shots of the day when he straight drove Turner into the timber-framed pavilion but Clare cut short what was developing into a dangerous partnership when he trapped him lbw in his first over.
Wadlan skied a sweep at Durston to mid-on but former Leicestershire wicketkeeper Tom New kept the Unicorns in the hunt against the county he played for on loan with 31 before he was caught behind in the 21st over.
When ex-Somerset stalwart Keith Parsons was run out for a duck in the same over, the Unicorns chase was faltering and Craig Park narrowly avoided matching his brother's first ball dismissal when he was dropped by Richard Johnson, who was making his debut on loan from Warwickshire.
Reece swept David Wainwright for six to reach 50 but when he sliced Turner to cover, the game was up and the fast bowler wrapped up victory with his fourth victim in the 39th over.