However his dismissal, coupled with some tight bowling from the spin trio of Mike Yardy, Will Beer and Chris Nash, meant the home side added only 48 in the next nine overs and looked unlikely to post a winning score when Matthew Wood was run out for 36.
But late impetus was added first by Chris Read (20) and then Sidebottom, who hit consecutive fours in the final over before holing out off the last ball of the innings.
Chris Nash (22) and Luke Wright (18) looked like making a big dent in Sussex's target until Wright was caught at mid-on off Darren Pattinson (3-17).
But despite the departure of the England all-rounder, the 2009 Twenty20 Cup winners did not look under pressure until Patel and Mullaney entered the attack.
First, Nash buckled after a string of dot balls to be trapped lbw sweeping at Patel, then Sussex captain Yardy was run out after a mix-up with Murray Goodwin.
After Ed Joyce also fell leg before, this time to Graeme White, Andrew Hodd joined Goodwin to try and launch a fightback.
But with every dot ball being cheered by the partisan home crowd, the contest was effectively ended when Hodd was well held at cover by David Hussey off Sidebottom, while Goodwin - who had already been put down twice - fell victim to an athletic Hales catch on the leg-side boundary.
Sussex were now left with far too much to do and, despite Keegan hitting the last ball of the match for six, Notts, runners-up in 2006, were celebrating reaching finals day for the second time.
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