When play began, Leicestershire were fourth in North Group, a point ahead of Derbyshire, Yorkshire and Durham, but their hopes of reaching the knockout phase were undone by Moeen’s dazzling knock.
He set the tone by hitting Josh Hull’s first two deliveries for four as he raced to 50 off 27 balls in an opening stand of 99 with skipper Alex Davies (31).
The left-hander struck nine sixes and seven fours before being caught off Hull at the start of the final over as Birmingham Bears posted a score of 194-5.
Leicestershire’s chase never got going after their first three wickets fell in the space of nine deliveries and Lewis Goldsworthy’s 35 was the only score of note as they were all out for 122 in 16.4 overs to lose by 72 runs – Danny Briggs taking 3-30.
Derbyshire Falcons scored quickly at the start of their innings against Durham but also lost wickets regularly and only managed a score of 155-8.
Durham, who began the match seventh in the table, approached their chase in controlled fashion and were 71-1 in the ninth over when spinner Alex Thomson sent back David Bedingham, caught by Samit Patel, for 15.
The visitors needed 81 from the final 10 overs and Lees and Ackermann did not need the final seven deliveries as an unbroken stand of 88 sealed an eight-wicket win on 159-2 – Lees finishing 72 not out from 60 balls and his partner on 54 off 30.