Sunderland-born Pringle’s superb 125 from 101 balls was the highest score by a Durham number eight in List A matches and saved the Jets from humiliation after they had collapsed to 75-7.
Usman Arshad helped Pringle add 62, a Durham eighth-wicket record in List A cricket, as the visitors recovered to 216, with Shiv Thakor and Andy Carter both taking three wickets for the Falcons.
But Pringle’s heroics were countered by Slater who marked his first 50 overs game for Derbyshire with 119 from 137 balls as the Falcons eased home with 8.2 overs to spare.
Pringle, 24, said: “We were easily a hundred short on that pitch.
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“There was a bit of spin and a little bit of seam movement, enough to keep everyone interested, but, in this day and age in 50 over cricket, 300 is probably not a match-winning score now.
“The game’s moving forward and you need to be getting 320, 330 plus to be confident of winning games.
“I don’t think the pitch did anything untoward – there was a bit of seam movement early on, but you expect that and I think if you ask the lads individually they might say there were poor shots on their part, but that’s the nature of the game.
“Once you get on a roll, as Derbyshire did, there’s a little bit of pressure with new batsmen coming in knowing it’s a white ball game and needing to score and, to be fair, once Derbyshire got on top they didn’t take their foot off.
“I didn’t really look at the scoreboard. We were behind the eight ball and I just thought if I could take a positive approach there were enough balls left and to get up to 200 was a great effort.
“But it was difficult in that middle period when they were on top and I certainly felt under pressure when I went out.”
Durham started strongly, with Mark Stoneman taking four fours from Carter’s second over, but the innings disintegrated in the face of some disciplined bowling on a two-paced pitch.
Phil Mustard was bowled playing no shot at Ben Cotton, whose opening seven-over spell cost only 10 runs and exerted pressure which forced poor shot selection.
Carter had the last word when Stoneman sliced to backward point and Graham Clark miscued a pull to midwicket as Durham limped to 38-3 from the opening powerplay.
The slide continued when Scott Borthwick was superbly caught by Neil Broom at second slip as he tried to run Thakor to third man and Paul Collingwood played across the line in the next over.
Calum MacLeod chopped Thakor into his stumps and Keaton Jennings reverse swept Matt Critchley to gully to leave Durham in disarray after 25 overs, but Pringle and Arshad began a fightback that started slowly and then moved into overdrive as Pringle launched a thrilling assault.
After Pringle completed his maiden List A 50 from 59 balls, Arshad was lbw to Thakor, but Pringle was now playing some inspired cricket and tore into the bowling with a salvo of powerful strokes.
Cotton was driven for four and lifted over long on for six before Carter was dispatched over the long off boundary in the next over.
Pringle drove Critchley down the ground for another four and two balls later, lifted the leg-spinner high over long on to reach an outstanding hundred which had transformed the contest.
He pulled Alex Hughes for his fourth six before he drove over a full length ball from Carter, but his stand of 62 from 37 balls with Chris Rushworth had set a Durham 10th wicket record against Derbyshire and given his team a chance.
But any momentum Pringle established was quickly removed as Billy Godleman and Slater took 62 from 10 overs and the opening pair continued to cruise with Godleman hoisting Borthwick over long on for six.
Although Godleman edged a drive at Arshad who also pulled off a stunning catch at mid on to remove Hamish Rutherford, Slater accelerated towards his century with two fours and a six from a Borthwick over before holing out two balls short of Derbyshire’s second win in the North Group.
Slater said: “I’ve not played many one-day games for the first team and that’s probably the best I’ve played.
“Billy played really well to get us off to a good start and to put a 100 on for the first wicket puts a massive hole into the 217 we needed. Billy batted brilliantly and then it was nice for me to kick on and get a big score.
“Probably over the last year or so I’ve not kicked on when I should have done so it’s been a long time since I last got a hundred for Derbyshire in the first team so it’s good to get over the line again, a weight off my shoulders really.
“With two wins from three in the Twenty20 and now two from two in this competition, the boys have been doing brilliantly. The bowlers at the top today to get them four or five down in the first 15 overs is invaluable because as soon as that happens you are always on the back foot.”