Notts Outlaws are out of the Clydesdale Bank 40 having been comprehensively beaten by Warwickshire Bears.
Jonathan Trott (84) and Ian Bell (50) helped the home side make light work of a victory target of 193.
Needing six to win, Ian Bell tried skied one to Steven Mullaney at mid-on but Troughton’s solitary boundary saw them to 194-3 to secure victory by seven wickets.
They will now face Yorkshire at Scarborough in the semi-final.
“Trott and Bell played very well and provided an excellent example as to how to chase down moderate totals,” said Nottinghamshire Director of Cricket Mick Newell.
“We needed to take early wickets to make our total defendable but we were unable to do that and they chased us down with very little pressure.”
Newell included Scott Elstone and Akhil Patel in his team as he maintained his policy to provide opportunities for young players.
“It was a difficult call to leave more experienced batsm out of the side but they haven’t fired in this competition when they’ve had opportunities and I wanted to back Scott and Akhil because they have done well when they have been in the side,” said Newell.
“Being eliminated from this competition won’t have any bearing on our Championship run-in and we’re pleased to be going through an entire season where we haven’t played any dead games.”
Alex Hales and Akhil Patel gave Notts a solid platform but Patel was caught by Ant Botha.
Adam Voges (54) prospered in the number three spot but Alex Hales hit straight to Troughton at long-on to fall for 34.
Samit Patel went for three as Warwickshire seized the initiative and Imran Tahir compounded their foothold by bowling Scott Elstone (5) to reduce Notts to 88-4.
Voges and Chris Read made fifty runs from 57 balls before steering Notts past 150 but Tahir’s wrist spin perplexed the Notts captain and the club’s fourth overseas player of the season.
Read was clean bowled and Voges stumped and when Paul Franks went for one, Notts were in trouble and were soon all out for 192.