The Sharks beat Middlesex by 31-runs to ensure a place in the last eight of the competition.
Sussex skipper Luke Wright said: "I felt it was a great effort by both teams to get the scores they did because the wicket was dying and keeping low, it was hard to hit boundaries when the ball got soft and I was delighted with the score we got.
"When Stirling and Simpson were going well I was worried but they still had to score at eight or nine an over and I felt if we kept our nerve and got those two out we could pile in and that’s what we did.
"It’s great just to be in the quarter-finals. We missed out on the last game last year but whoever we play we’ll fancy our chances. There are some good teams in the North Group but we’re not a bad side ourselves and we’ve won three games this week so maybe we’ve got some momentum just at the right time."
Sussex spinner extends Hove stayMiddlesex coach Daniel Vettori said: "We’ve run the whole gamut of how to lose T20 games this season. We were poor at the start with the ball tonight, but managed to drag it back on a small ground with a tiny boundary to defend.
"When we batted we had it comfortably in control but losing four wickets in two overs when you have to face Mills, Jordan and Archer at the death you almost have to kill the game before that happens and we killed the game for ourselves rather than in a positive way."