Durham 159 for 2 (Lees 72, Ackermann 54) beat Derbyshire 155 for 8 (Sowter 2-18, Raine 2-19, Parkinson 2-33) by eight wickets
Lees made 72 off 60 balls and Ackermann 54 from 30 with the pair sharing an unbroken stand of 88 as Durham ended on 159 for 2 to claim the remaining quarter-final place in the North Group.
Most of the Falcons got a start on a slow pitch but no one could go on with Wayne Madsen and Alex Thomson top scoring with 22.
The home side fought hard to defend a modest total but Lees and Ackermann showed experience and nous to take Durham into the knock-out stages.
Falcons had motored to 64 in the powerplay with Paul Coughlin leaking 33 from two overs but their adventure came at the cost of three wickets.
Luis Reece went in the first over, bowled stepping across to Parkinson before David Lloyd cut Coughlin for four and six.
Aneurin Donald drove Parkinson over the long off boundary but then top edged a sweep to backward square.
Coughlin was cut over third man for six by Madsen but responded by having Lloyd caught behind for 20.
Madsen made a brilliant century against Durham in the Blast two years ago so they were relieved when he mistimed a drive at Sowter and holed out to long off to leave the Falcons 65 for 4.
Coughlin returned to have Brooke Guest caught behind and his next ball saw Ross Whiteley edge to slip where Ashton Turner spilled the chance.
Samit Patel cut Matthew Potts over third man for six but Sowter was tying the Falcons down and he struck again when he trapped Patel lbw for 20.
When Whiteley edged a drive at Raine, Falcons were 110 for 7 but Thomson pulled Coughlin for six before Mohammad Amir smashed Parkinson into the front of the media centre.
Raine bowled Amir as he and Potts conceded only 15 from the last three overs to leave Durham chasing 156.
Lees drilled Daryn Dupavillon for two fours but Amir was giving nothing away, conceding only five from his first two overs before taking a smart catch at short third off Pat Brown to remove Graham Clark.
Lees pulled and drove Amir for two fours to take Durham to 45 for 1 at the end of the powerplay but they were being made to work hard by some disciplined bowling.
Although David Bedingham pulled Thomson for six, he dragged the next ball to mid-wicket and after 10 overs, Durham were 75 for 2, needing another 81.
Ackermann eased the pressure with two big sixes over midwicket off Thomson in the 13th over and drove Reece for another off the last ball of the 15th.
Patel conceded only four off his final over but Lees and Ackermann took no risks to see Durham home with seven balls to spare.