Hibs wasted no time to open to score as Ryan Porteous met a corner-kick in the eighth minute to nod the Edinburghers ahead at the Ibrox.
It wouldn't be long before Rangers levelled things up, however - former Liverpool forward Ryan Kent set up Fashion Sakala, who danced by a few defenders before slotting home after a quarter of an hour.
Celebrations were cut short for the home side less than 60 seconds later, when Kevin Nisbet pounced on a loose ball in the Gers' box and fired it into the roof of the net.
The match simmered down for the remainder of the first period, but Rangers looked the more likely to score.
The home side would get their reward just before 60 minutes as Ryan Jack found undone Hibs to make it 2-2.
Just four minutes later, the Gers took the lead for the first time in the match through star striker Morelos, intelligently assisted by Malik Tillman.
Get all of Flashscore's statistics and commentary from the match here!
Rangers now sit six points behind bitter rivals Celtic in the SPFL, though the Hoops are in action against Aberdeen this weekend. Hibs remain eighth on 20 points.
