Celtic's second was a piece of counter-attacking artistry. Nicolas Kuhn set the champions galloping off with a fabulous pass on the edge of his own box to unleash Jota, who switched play to Engels on the right.
The Belgian moved into the area and returned to Jota to scoop into the net.
Jeppe Okkels wasted another enticing Aberdeen opening, blasting straight into Alistair Johnston, before McGregor's ruthless side-foot finish piled on the misery.
The second half yielded few chances, Maeda menacing from Reo Hatate's curler, Aberdeen's Morris rolling tamely wide after robbing Auston Trusty and haring into the box, before Toppi Keskinen ran himself into trouble rather than shooting.
Typically, Celtic made them pay, Luke McCowan sliding in Yang Hyun-jun to stab past Ross Doohan from six yards.
Now lacking in gumption, Aberdeen were a broken team.
Their last act of defiance came when Morris overpowered Liam Scales and shot through Schmeichel from a tight angle, who whacked a post in frustration at a clean sheet now stained and record ripped from his grasp.
As if stirred by the concession, Celtic had the final say, Maeda knocking in a terrific Johnston cross in stoppage time.
Aberdeen remain a solitary point above Dundee United, who host Hibs on Wednesday, while Celtic's procession towards another title continues apace.