The visitors piled up 220 for six, their second-highest Blast total, built upon an opening stand of 126 in 68 balls from Graham Clark (65, 40 balls, seven fours, three sixes) and Tom Latham (58, 34, four fours, four sixes).
Chasing 200-plus for the second time in 48 hours, the Bears lost Ed Pollock to the second ball of the innings as Will Smith opened with a wicket-maiden.
Sam Hain (95, 53, seven fours, five sixes) and Colin de Grandhomme (62 not out, 32 balls, four fours, five sixes) kept their hopes alive into the closing overs but finding 35 from the last two proved too much and the Bears ended on 202 for five.
The Jets' second win of the tournament keeps them right in the qualification race.
Birmingham are still in there too but need to bounce back from back-to-back home defeats which brought heavy punishment for their bowlers.
Durham chose to take first use of a good batting track and Clark and Latham amassed the Jets' record T20 opening stand.
Clark was first to 50 (31 balls) when he hoisted Oliver Hannon-Dalby into the Hollies Stand. In the next over a Latham six off fellow New Zealander Grant Elliott brought the 100 up from 9.3 overs.
Birmingham hit back with four wickets for 12 runs in 14 balls. Latham was held by Dom Sibley at extra-cover, James Weighell and Liam Trevaskis holed out and Clark clipped Elliott to short fine-leg.
The Jets' dominance was reasserted by a ferocious stand of 75 in 33 balls by Paul Collingwood (37, 22 balls) and Smith (34, 17). Collingwood took the bulk of 27 from a de Grandhomme over which summed up the Bears' bowling problems with several balls failing to pitch.
Birmingham required 11 an over to win but were four for one after two overs, Pollock having lifted to long leg.
Ian Bell flicked Nathan Rimmington to short fine leg then Smith, having rested with figures of 1-1-0-1, returned to have Adam Hose caught at deep cover.
Hain kept his side afloat before a counter-attack was heralded by four successive sixes by De Grandhomme off Imran Tahir.
Hain hit 29 from a Chris Rushworth over and the fourth-wicket pair added 100 in 50 balls to keep their side in the hunt with 52 needed from four overs.
However, Weighell returned to bowl the first of those and did so superbly, Hain and Elliott holing out from the first and last balls to leave 49 required from three.
It proved too many - Birmingham's bowlers had given their batsmen too much to do.
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