Abada put champions Celtic ahead in the eighth minute with a low shot from the penalty area into the bottom corner following a cross from Matt O'Riley.
Rangers wasted a chance to equalise in the 23rd minute and it proved to be costly as winger Jota doubled Celtic's lead, lifting the ball over the goalkeeper and into the far corner in the 32nd minute following a brilliant pass from O'Riley.
Abada completed his double in the 40th minute when his low strike whizzed through the legs of Rangers goalkeeper Jon McLaughlin, sending the fans at Celtic Park into a frenzy.
David Turnbull finished the job with a 78th-minute goal, thanks to an error from keeper McLaughlin after he passed the ball straight to the Celtic midfielder, who easily rolled it into the net.
Celtic, who have won all six Premiership games this season, will next host Champions League holders Real Madrid in their first group stage match on Tuesday.