January 19, 2017 0429 GMT
To compound City's woes, as manager Manuel Pellegrini's decision to field a strong side just four days before a Manchester derby backfired, key playmaker David Silva limped off injured early on, pressassociation.com reported.
But after a dismal start to the season, Newcastle and Alan Pardew are suddenly enjoying a mini-revival with three successive wins all competitions easing the pressure on the under-fire manager.
Aarons stunned City when he capitalized on poor defending early on and the host, despite controlling possession and creating some chances, never truly convinced.
Newcastle was denied what seemed a clear-cut penalty in the second half but Sissoko finished the job 15 minutes from time, loosening City's grip on the trophy with a fine finish.
Pellegrini's men have now gone three games without a win and need to regroup with two big games in the next week against United in the Premier League and CSKA Moscow in the Champions League.
Losing Silva, who was surprisingly not granted a rest along with likes of Joe Hart, Vincent Kompany and Aguero, made for a dismal start.
Silva was injured when fouled by Ryan Taylor, making a welcome first Newcastle appearance in two years after overcoming cruciate ligament trouble, on the edge of the area.