At Derby, Samit Patel was hoping to sign-off with a win in his final game for the Falcons but he endured a miserable evening as the Bears sealed their qualification with a commanding victory.
Latham (104 off 51 balls, with eight sixes) and Davies (89) shared an opening partnership of 187 – the joint-fourth highest in the Blast – as the visitors piled-up 233-5 with Patel finishing with 0-38 from his three overs.
Derbyshire were quickly reduced to 62-5 in reply as Patel fell for six and they subsided limply to 106 all out to finish bottom of North Group.
“We probably saved our best performance for when it mattered most in a must win game so to get that big score on the board was really pleasing,” said Bears head coach Ian Westwood.
“It was a special knock (from Tom Latham) – he’s shown glimpses this campaign without really going on to get that big one but that’s why you get great players who are experienced like Tom.”
Northamptonshire skipper David Willey crashed six sixes in his 32-ball 63 and Matthew Breetzke made a rapid 52 as the Steelbacks threatened to derail Durham’s qualification hopes at Chester-le-Street.
But the home side made light work of their victory target of 204 to jump up to second place and earn a home tie.
Alex Lees (101* off 49 balls, with eight sixes) and Graham Clark (79 off 41) shared an opening stand of 181 as Durham coasted to victory with three-and-a-half overs to spare.
Young off-spinner Ahmed stole the show for Nottinghamshire as the Outlaws picked up a consolation five-wicket win over Lancashire at Trent Bridge.
The 17-year-old younger brother of England’s Rehan Ahmed claimed the third hat-trick of this year’s Blast by removing Luke Wood, Tom Aspinwall and Mitchell Stanley as he returned figures of 5-25.
Leicestershire also held an outside chance of sneaking into the last eight but needed to beat Yorkshire and hope for some help from elsewhere – neither of which happened with Matt Milnes hammering the last balls for six to seal a dramatic win for the visitors at Grace Road
Abdullah Shafique again impressed with the bat for the White Rose as his 64 anchored them to victory, helped by 52 from Matthew Revis before Milnes’ late fireworks ensured Yorkshire avoided finishing bottom of the table.