A 68-run stand between Callum Ferguson (47) and Chris Green (34 not out) ultimately counted for little and the battle for the last spot in the finals is now down to fourth-placed Brisbane Heat and fifth-placed Melbourne Stars.
If the Stars defeat Sydney Sixers on Sunday, when the MCG hosts the final match of the regular season, they will leapfrog Brisbane on the ladder.
The prospect of Brisbane progressing will burn deeply for the Thunder, who unsuccessfully lobbied Cricket Australia in pursuit of the full points after the Gabba lights went out during their clash with the Heat.
Cummins and Khawaja, fresh from starring in Australia’s dominant Test win over Sri Lanka at Manuka Oval, once again stepped up in the nation’s capital.
Cummins finished with 2-28 and could easily have captured the scalps of the BBL’s two leading run-scorers in his first over.
The express paceman hit the top of off stump to dismiss Short for seven and would have ended Wade’s knock in the same over if Fawad Ahmed held a catch in the deep.
Wade was eventually caught behind on 45 but a 94-run stand between George Bailey (53) and Ben McDermott (44 not out) proved a hammer blow to Sydney’s finals hopes.
Earlier, Wade was dropped on five and 14 by Fawad before a brief rain delay reduced both innings by one over.