The fast bowler took 5 for 56 to restrict the Falcons to 297 for 8 which was built around Billy Godleman’s 116 and 88 from Luis Reece.
Former Derbyshire opener Ben Slater scored 83 on his return to Derby and although 18-year-old paceman Alfie Gleadall bagged three wickets, Steven Mullaney with an unbeaten 68 and 52 not out from Tom Moores guided the Outlaws to 299 for 4 in the 46th over.
The Falcons looked on course for 350 after Godleman and Reece accumulated steadily on a pitch lacking in pace and bounce.
Fletcher beat the bat several times in a probing spell but there were few problems for the openers with Reece ending a lean start to the season by reaching his first 50 off 52 balls.
Godleman needed 86 balls for his second consecutive half-century and the Outlaws had to wait until the 31st over for the breakthrough which came when Reece top-edged a sweep at Mullaney.
Wayne Madsen lifted the scoring rate with 38 from 28 balls until he was deceived by a good slower ball from Jake Ball who bowled intelligently to check the Falcons progress.
Godleman drove Fletcher for six but the fact his century came off 131 balls highlighted the slow nature of the pitch and the accuracy of the bowling.
Another well disguised slower delivery from Ball removed Matt Critchley and after Leus du Plooy was bowled advancing at Fletcher, Godleman was caught behind in the 49th over.
Alex Hughes pulled Ball for six but Fletcher bowled straight and full to strike three times in the final over to keep the Falcons under 300.
It did not look enough as Slater and Joe Clarke plundered 70 from the first 10 overs with Clarke cutting Mark Watt’s left-arm spin for three consecutive fours.
But Gleadall tempted Clarke into a skied pull to deep mid-wicket and Ben Duckett played across Reece in the next over.
Slater and Jake Libby swung the initiative back towards the Outlaws by working the ball around to add 93 before Gleadall returned to revive the Falcons hopes with a double strike in the 30th over.
Slater drove loosely to cover and three balls later, Libby got a top-edge trying to turn it to leg and was caught at mid-wicket for 41 to leave the Outlaws on 173 for 4.
Moores responded by driving Gleadall and Watt for sixes, Mullaney twice deposited Watt high over long on before Moores smashed Gleadall for two more sixes to reduce the target to 56 from the last 10 overs.
The chase turned into a stroll in the evening sunshine as the pair sealed victory with 29 balls to spare.