It leaves the current Blast champions on top of the North Group with seven wins from 11 and virtually assured of a quarter-final place.
Ball hailed the result and said he felt he has more to come, saying: "We've got a lot of players that love the big occasion, we are used to playing in front of big crowds at Trent Bridge with a good atmosphere, so it does feel quite nice at Edgbaston and we handled it really well.
"The batters put on an amazing score which we thought was above par. The opening stand from the guys put us in a strong position and really set up the win.
"I feel like I am getting there. I am probably not quite 100 per cent but me and Fletch have been working together to see what we can do to keep improving because every year teams are coming back and trying something different.
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"It's a great achievement for us to be top of the group and I think the biggest achievement is to have won the last two games despite missing three key players. That shows our strength in depth."
The Outlaws totalled177 for nine thanks to Samit Patel (41, 30 balls), Ben Duckett (39, 20 balls) and Alex Hales (34, 21 balls) against a depleted attack.
The Bears' reply then plunged into disarray at 19 for five and they were bowled out for 63, their lowest ever T20 total, as Jake Ball took three for 10, Calvin Harrison three for 12, including a triple wicket maiden, and Samit Patel two for eight.
Having taken 18 wickets at 13.33 apiece in the tournament, Brathwaite was a big loss to the Bears' bowling and Notts, put in, set off in a manner to take full advantage. Opening pair Duckett and Hales smashed 54 in boundaries in a stand of 75 before both fell to superb catches.
Duckett was brilliantly caught by Matt Lamb at deep cover off Danny Briggs and Hales was well-held by Sam Hain running round the long on rope.
The introduction of spinner Lintott applied a brake and, though Patel batted with his customary verve, Notts were grateful for a late salvo of 18 in six balls from Harrison.
The Outlaws then torpedoed the Bears' reply right at the top with three wickets in the first 17 balls. The spinners gave their side the perfect start as Patel dismissed Adam Hose, caught and bowled, in the first over and Matt Carter conceded just a single from the second.
Ball delivered the third and ended it with 1-0-4-2 after Will Rhodes lifted to mid on and Ed Pollock dragged a pull on to his stumps. Patel and Ball had not finished, foxing Hain and Lamb into sending up skiers to leave the innings in ruins at 19 for five.
Rob Yates and Michael Burgess took the score to 39, but a triple wicket maiden from Harrison, ousting Burgess, Tim Bresnan and Briggs, turned that into 39 for eight.
Rapturous applause from the big, good-natured crowd greeted the raising of the 50 but the Bears still have much work to do to qualify while The Outlaws are pretty much there with three games to spare.