Nottinghamshire 212 for 5 (Moores 80*, Libby 58) beat Yorkshire 149 for 7 (Kohler-Cadmore 72, Willey 30, Gurney 3-24) by 63 runs
Both youngsters registered their highest scores in the competition, as Notts posted 212 for 5 on their way to a victory by 63 runs. Moores scored an unbeaten 80, blasting six fours and three sixes, putting on 112 in only 10.5 overs with Libby, who made 58.
The Vikings were always struggling to compete with a rapidly-increasing run-rate and could only make 149 for 7. Tom Kohler-Cadmore top-scored with 72 in their chase but the Outlaws' attack held firm, led by Harry Gurney's 3 for 24.
Yorkshire lacked skipper Steve Patterson and Tim Bresnan from the side beaten by Lancashire and their injury concerns are also piling up. Patterson, their seasoned seamer, whose unexpected rise to the captaincy late in his career has brought a semblance of stability, will miss the rest of the season with a broken finger; David Willey took over here.
And a hand injury to Kane Williamson in this match - like Patterson the previous day, also while taking a catch - will mean an anxious wait while x-rays are assessed.
Libby said: "They haven't quite found the balance of the batting order right yet and they gave me the opportunity to bat at three tonight. I enjoyed it and tried to play strong shots. You get value for your shots here."
At the start of the evening Alex Hales, playing his 100th T20 game for his county, fell for 17 in only the third over of the match, cutting Jack Brooks to point, where Williamson took a low catch. The New Zealander immediately left the field and didn't return for the remainder of the innings, requiring attention to a hand injury.
Libby was the chief aggressor as the two youngsters began their stand. The Cornishman cleared the ropes for the first time with a mighty blow off Brooks and repeated the dose off Jordan Thompson to bring up the 50 stand.
Both batsmen continued to pepper the Vikings attack in their personal duel to reach 50 and it was Libby who arrived at the landmark first, from only 25 balls. Moores followed, getting there from 35 deliveries.
Thompson ended the stand by bowling Libby but the runs continued to flow as Dan Christian plundered 20 from only seven balls. Moores and Samit Patel took 14 from the final over to set the Vikings a challenging target.
Adam Lyth, playing his 100th T20 match, made only 14 but it was the only success for Notts in the opening 12 overs as Kohler-Cadmore and Willey added 74 together; Riki Wessels' fine boundary catch off Patel ending the partnership.
Ish Soshi bagged the prize scalp of Kohler-Cadmore, with Steven Mullaney taking the catch and then Gurney claimed his three wickets to seal the win.
Amongst his haul was the wicket of Williamson, who made his way to the crease at No. 5 but was clearly handicapped by his injury and could only make 11.
Four wickets fell for only five runs in the closing stages, leaving 70 runs needed from the final over.
The margin of victory, in front of a crowd of 12,277, leapfrogs Notts above Yorkshire and into four place in the North Group.