Fresh from breaking two scoring records with his double against Feyenoord in midweek, the Colombian has now netted in every one of his last 10 starts for Steven Gerrard's side after nodding them ahead 12 minutes in.
Much has been made this week about the striker's potential transfer value but in this form his real worth is simply priceless for the Light Blues.
The victory meant Rangers kept stride with Celtic at the top of the table, with the Hoops just one goal better off than their bitter rivals.
Hearts themselves remain locked on the same points as bottom duo St Johnstone and St Mirren.
But this was another abject performance that must now put to bed any faint hope interim manager Austin MacPhee had left that he might be able to persuade Tynecastle owner Ann Budge to give him the job permanently.
In his first game as caretaker during last month's Betfred Cup semi-final with Rangers, MacPhee had left Uche Ikpeazu on the bench in the hope he could make a later impact. It did not work as the Ibrox side cruised to victory.
This time the powerhouse frontman was in from the kick-off but he made barely a dent on the home defence.
Instead it was mostly one-way traffic towards Joel Pereira's goal.
Gerrard was unhappy with referee Don Robertson's decision not to award his side a penalty 11 minutes in when Glen Kamara was shoved in the back by Jamie Walker.
But Gerrard was smiling 60 seconds later as his team grabbed the lead.
The hosts refused to relent on the back of that unsuccessful spot-kick appeal, with Kamara working the ball out left for Borna Barisic.
The Croatia left-back's delivery was on the money and in a repeat of Rangers' second goal against Feyenoord, Morelos got in between two defenders – this time Aaron Hickey and Oliver Bozanic – to bullet home with his head.
He was unlucky not to grab a second on the half-hour mark as Pereira made a block at point-blank range but there was a feeling the hosts had allowed their tempo to drop.
Hearts created their only opportunity of the first period in the 36th minute as Jamie Brandon drove to the by-line but Ikeapzu could only fire wide on the stretch.
If that half chance gave the Jambos hope, it was immediately snuffed out as Rangers doubled their lead a moment later.
Scott Arfield and Joe Aribo had been brought back in by Gerrard, with Arfield the man surprisingly starting in the centre of midfield with Aribo out wide.
But the change of roles made no difference as Arfield measured a ball in behind for the former Charlton midfielder, who cut back inside before serving the ball up on a plate for Kent to sweep home.
The opening quarter-hour of the second half saw the Hearts goal live a charmed life.
But the visitors could only stem the tide for so long and found themselves three down after 64 minutes.
Steven Davis release James Tavernier down the right. The Rangers skipper was aiming for Morelos but Berra – aware the striker was behind him – stuck out a leg and watched with horror as the ball dribbled into his own net.
It got worse for Hearts in the final 10 minutes.
First Sheyi Ojo robbed Hickey on the by-line before cutting inside to shoot. Pereira saved that effort but was helpless as substitute Stewart slotted home on the rebound.
The keeper failed to cover himself in glory five minutes later as he allowed Stewart to head home at the second attempt as the ball squirmed through his grasp and over the line.