The West Indies left-hander struck a brilliant unbeaten 87 from just 70 balls to see the home side to a third win in as many games with three balls to spare at Derby.
Lancashire had set the hosts 152 for victory on the back of Karl Brown's half-century, but were ultimately made to pay for a sluggish start with the bat as the wet weather held off for long enough to get a full game in.
Rain abated 45 minutes before the scheduled start time, allowing play to commence just five minutes late - although the visitors must soon have been wishing for another downpour as they were reduced to 19 for three after losing the toss.
Stephen Moore had already seen one top-edged pull fall safe in Tim Groenewald's opening over, but was not so lucky the second time as his skied miscue gave wicketkeeper Tom Poynton plenty of time to snaffle an easy catch.
Steven Croft then fell for a duck playing the same shot to the same bowler and Ashwell Prince became Groenewald's third victim at the start of the fifth over - Jonathan Clare taking a sharp low catch at short midwicket.
Simon Katich initially set about repairing the damage, although he was lucky to survive an appeal for caught behind off Mark Footitt's first ball as umpire Neil Bainton adjudged the ball had struck only the Australian's arm, with replays suggesting it had hit the glove as well.
The left-hander made the most of his reprieve, plundering two fours and a six from the rest of the unfortunate Footitt's over. Katich's luck then ran out when he was lbw, for 28, to a Clare delivery that looked to have pitched outside leg.
Brown had been the quiet partner with Katich at the crease, but took up a more aggressive role when adding 68 for the fifth wicket with Tom Smith.
Lancashire’s run-rate improved as a result of that stand, which ended when Smith was caught at long-off facing Dan Redfern.
The off-spinner’s next ball was thumped over long-on by Brown, yet Redfern got his revenge by holding a catch when Lancashire’s top-scorer attempted to clear the same boundary off Wes Durston.
Wicketkeeper Gareth Cross provided some late impetus with two big sixes off Redfern's penultimate over; both shots landing on the roof of the hospitality tent.
Cross was also dropped by Footitt, but the left-arm seamer atoned for the error by catching Kabir Ali on the cover boundary as Groenewald completed figures of 4-21.
Glen Chapple was run out from the final ball of the innings, but Derbyshire’s reply started dismally when Chesney Hughes flashed an edge to slip from the first ball of the innings, bowled by Kabir.
Chanderpaul and skipper Durston steadied the ship with a 50-run partnership before the latter played on to Chapple at the end of the six-over powerplay.
By that stage the home side were well ahead of the Duckworth/Lewis par score, helped by Chanderpaul's scooped six off Kabir and Durston's glanced maximum off Chapple.
Chanderpaul and Wayne Madsen continued to steadily accumulate thereafter and although rain briefly halted proceedings, play soon resumed with no overs lost.
The impressive Smith had gone for just one run in each of his first two overs, and made a valuable breakthrough at the start of the 15th over when Madsen's cut was brilliantly taken by a diving Moore at cover.
At 96 for three Derbyshire were suddenly behind on D/L, prompting the promotion of big-hitting South African Albie Morkel to number five.
It was Chanderpaul, however, who kept Derbyshire's chase alive when taking 17 off Stephen Parry in the 16th over, with the aid of a switch-hit four and a more orthodox maximum.
Morkel got in on the act by pulling the first ball of Smith's next over to the midwicket fence, and fittingly it was Chanderpaul who finished the job with consecutive boundaries off Kabir, taking Derbyshire top of the North Group.