The two Derbyshire all-rounders struck four sixes each as the Falcons posted the fifth highest total in Twenty20 matches. Gavin Griffths, who took four wickets against Lancashire the night before, added one more but conceded 26 in an over for figures of one for 49 from three.
Critchley then took two for 31 with his leg breaks and Netherlands pace bowler Logan Van Beek three for 37 as the Foxes were bowled out for 186 in 19 overs to lose by 23 runs, Rishi Patel top scoring with 35 off 20 balls.
Falcons match-winner Matt Critchley, whose 80 not out was a career-best, said: “It was one of those days when everything came off, especially towards the end.
“There can be pressure when you are chasing so potentially it can be better to bat first and we knew we had got more than a good score.
“After having a couple of setbacks, with Benny McDermott not able to play and Wayne Madsen injured, it was great to get that first win on the board and though it has been a while coming the belief within the squad has never wavered.”
After Derbyshire were asked to bat, Foxes fans were soon enjoying the sight of Naveen bamboozling batsmen with his heavily disguised slower balls, the 21-year-old dismissing debutant Harry Came and Derbyshire skipper Billy Godleman in his first two overs.
Came - in for the injured Wayne Madsen - miscued to mid-on before Godleman, despite all his know-how, was left groping for another floaty delivery that bowled him.
Two of Reece’s sixes came in the Powerplay as the Falcons advanced to 52 for two, after which Leus du Plooy was soon caught behind off a wide ball from off-spinner Arron Lilley.
Reece, dropped on 50, had added only a single when a Griffiths yorker beat his attempted reverse sweep but if Leicestershire imagined they had made the decisive breakthrough they were mistaken as Critchley and Alex Hughes added 85 from 47 balls before Hughes holed out to long on for 38.
Naveen avenged a huge six from Fynn Hudson-Prentice by having him caught off a miscue next ball but could not stop Derbyshire recording their highest score against Leicestershire in this format.
After the Foxes lost Scott Steel first ball, Lilley boldly tried to keep the required rate in reach by smashing 29 from 20 balls but then found the fielder at long-on and being eight ahead on the Powerplay score was tempered for the Foxes as Josh Inglis was well caught at deep mid-wicket to the last ball of the sixth over.
Ackermann and Lewis Hill were dismissed in consecutive overs and though Patel and Ben Mike attempted to keep their side in theoretical contention, they too fell in consecutive overs, after which Critchley dismissed Naveen and Will Davis for ducks in the same over before Van Beek wrapped things up by having Griffiths caught at long-off.