Steven Gerrard's side dropped points for only the fifth time this season after Mohamed Elyounoussi put Celtic ahead, but Rangers remains undefeated in its top-flight championship campaign.
The usual hostilities were put aside during a show of pre-match unity from both teams, in response to Rangers midfielder Glen Kamara being allegedly subjected to racist abuse during a midweek UEFA Europa League defeat to Slavia Prague.
However, Morelos customarily ensured some of the old devilment remained when he scored in the league derby at the 13th time of asking – holding up 10 fingers in celebration to mock Celtic failing to a win a record-breaking 10th consecutive title this season.
Celtic, playing under caretaker manager John Kennedy, deserved its 23rd-minute breakthrough.
Callum McGregor slid a pass in behind Rangers right-back Leon Balogun and Odsonne Edouard's superb left-footed cross was matched by Elyounoussi's full-length diving header.
Edouard tormented Balogun and the rest of the Rangers defence at times, although referee Willie Collum adjudged him to have dived under a sprawling challenge from Borna Barisic and dished out a yellow card before the half hour.
The visitors were level in the 38th minute, Balogun atoning for his part in the opener by rising highest to meet Barisic's corner and leaving Morelos with the formality of nodding home unmarked at the far post.
That sparked a flurry of activity at both ends before half-time as Allan McGregor recovered to retrieve an Edouard effort that squirmed through his legs, before opposite number Scott Bain in the Celtic goal kept out a sublime Ryan Kent volley.
Rangers continued to look vulnerable to set-pieces, with Elyounoussi and Stephen Welsh going close either side of the interval.
McGregor was equal to an Edouard long-range effort and then thwarted David Turnbull in the 72nd minute after the midfielder was played in by Ryan Christie.
Unsurprisingly, Edouard reacted quicker than any Rangers player to the resulting corner, but Gerrard's men kept their unbeaten league record intact.