The Phoenix's home ground remains a fortress - they have yet to lose a game there - after a vibrant bowling and fielding display set up their third successive win in this year's competition.
They had the Rockets reeling at 53 for six before a bold unbroken stand of 92 in 46 balls from Daniel Sams (55, 25 balls) and Luke Gregory (35, 22) took the visitors to 145 for six. Benny Howell continued his fine form in the tournament with three for 28.
The 15,800 crowd then raised the Edgbaston roof as skipper Moeen Ali smashed 52 in 28 balls with five sixes to power his side towards victory with 14 balls to spare. Liam Livingstone's unbeaten 51 (32) saw his side home despite Luke Wood's impressive three for 16 from 20 balls.
Put in, the Rockets lost big-hitters Alex Hales, who lofted Moeen to deep mid-wicket, and Dawid Malan, caught at long off off Imran Tahir, in the first eight balls. The rest of the top order also misfired in the face of excellent fielding and deadly bowling from Howell.
Colin Munro fell to a superb return catch from Tom Helm while Howell dismissed Samit Patel, smartly taken at cover by Moeen, Tom Kohler-Cadmore, bowled through a slog, and Ian Cockbain, lbw.
That left the Rockets in deep trouble at 53 for six from 54 balls but Sams and Gregory responded to the crisis with brio. Australia international Sams cracked five fours and three sixes, supported by the Rockets' skipper (two fours and two sixes) to keep their side competitive in the game.
They were even more competitive when Luke Wood bowled Will Smeed with the second ball of Phoenix's reply. Wood then trapped Miles Hammond (20, 16 balls) lbw but Moeen launched a fierce counter-attack. He took 23 off a Gregory over including two runs from a big slice of luck when he skied to extra cover but Malan lost the ball in the floodlights and it fell to earth a short distance from him.
Birmingham-born Moeen sped to a 26-ball fifty before Wood returned to hit his middle stump. Wood's discipline with the ball was not matched by his colleagues in the attack, however, and experienced pair Livingstone and Matt Wade, left to find 36 from 34 balls, made light of the task to keep the Phoenix fortress unbreached.
Livingstone ended the match in style, reaching his fifty with the winning runs - another towering six.