|Vitality Blast, Trent Bridge|
|Middlesex 160-8 (20 overs): Morgan 53; Carter 2-16|
|Notts Outlaws 165-0 (16.2 overs): Hales 83*, Nash 74*|
|Notts Outlaws beat Middlesex by 10 wickets|
Notts Outlaws thrashed Middlesex by 10 wickets to reach their third T20 Blast Finals Day in the past four seasons.
Alex Hales (83 not out) and Chris Nash (74 not out) made light work of a target of 161 as the hosts coasted to victory with 22 balls to spare.
Eoin Morgan's 53 off 31 balls was the mainstay of Middlesex's 160-8 but early wickets left them in trouble at 43-4 with AB de Villiers making just 11.
Notts, who last won the trophy in 2017, join Essex Eagles at Finals Day.
Hales, omitted from England's World Cup-winning squad earlier this season following suspension for off-field matters, will head to the Caribbean Premier League to play for Barbados Tridents on Friday.
The right-hander will return in time for the T20 Blast semi-final at Edgbaston on 21 September.
He smashed six fours and seven sixes in his 47-ball knock while Nash, named in the side for the first time this year in the competition, hit 10 fours and a six in his 53-ball blitz.
Middlesex had not reached the quarter-finals since 2015 and had a night to forget in their first meeting with Notts in T20 cricket.
They lost openers Paul Stirling and Dawid Malan as well as de Villiers and Stephen Eskinazi inside the first seven overs after losing the toss and being put in.
Morgan rebuilt with the help of John Simpson (25) and Toby Roland-Jones (26), but fell a ball after reaching his half-century as Middlesex tried to set an imposing target.
Any chance 161 would be too much for Notts to chase evaporated as Hales and Nash plundered 76 without loss inside the powerplay.
They also profited from sloppy Middlesex fielding, with Nash dropped on 31 and Hales twice put down on 47 and 56.
Hales' seventh sixth brought the curtain down on a commanding win with more than three overs remaining.
The two remaining quarter-finals see Sussex Sharks face holders Worcestershire Rapids on Friday in a repeat of last year's final before Gloucestershire and Derbyshire meet at Bristol on Saturday.
Notts Outlaws captain Dan Christian told BBC Radio Nottingham:
"That was pretty close to the perfect game. We've been looking for that all tournament and if you pulled apart every ball, you'd hardly be able to find many faults with our game.
"Early wickets in the powerplay always helps and it put them under pressure because we tried to make them take risks.
"It's been tough to have somebody Like Chris (Nash) on the sidelines throughout and difficult to get him in the team, but it was a decision we felt we had to make and luckily it paid off.
"Alex (Hales) has been getting better and better and this was him back to his best."
Middlesex captain Dawid Malan:
"Pretty much everything went wrong for us, starting from losing the toss. It's disappointing the way we lost early wickets, twice we lost two in a row and 43-4 wasn't good enough.
"Even though, we felt we had a sniff with 160 on the board if we bowled well in the first six overs.
"It wasn't a bad wicket, but we misread it."