The Colombian became the first Rangers player to score in four consecutive European clashes when he cancelled out Jans Toornstra's opener in Rotterdam.
Morelos then left De Kuip stunned as he struck his 13th European goal of the campaign shortly afterwards to smash Henrik Larsson's 16-year-old record for the most goals netted in a single season for a Scottish club.
There was further disappointment coming from Berne where Porto – who had to match Rangers' result to deny the Scots qualification with a game to spare – came from a goal down to snatch victory against Young Boys.
However, the Light Blues did move to the top of Group G and will seal qualification with a draw against the Swiss outfit at Ibrox in a fortnight's time.
It was past versus present on the touchline as former Ibrox boss Advocaat came up against current incumbent Gerrard.
Most were expecting fireworks on the field but the game would have been hard-pushed to match the spectacular firework display launched from behind the stand housing the Feyenoord ultras before kick-off.
The Rangers faithful responded with a show of banners and flares, which is likely to lead to a UEFA investigation, but how Gerrard had wished his side had possessed even a fraction of that explosiveness during the opening half.
The closest the visitors came to troubling Feyenoord goalkeeper Nick Marsman was in the second minute as Morelos poked the ball wide after Ryan Kent had led an early breakaway.
But creativity was in short supply as the hosts gradually took control.
There was some good news as Young Boys took the lead against Porto but Gerrard would have been much more concerned with what was going on in front of him as Feyenoord regularly raided down his team's flanks.
There was a nervousness that seemed to grip Rangers whenever they faced a set-piece delivery. That was evident as early as the 18th minute when Filip Helander was slow getting off the ground, allowing Eric Botteghin to connect with Orkun Kokcu's corner.
Allan McGregor produced a brilliant stop to keep the scores level before Leroy Fer's rebound attempt clipped a post on its way to safety.
But luck was against Gers in the 33rd minute as Feyenoord struck.
Borna Barisic did his team no favours as he headed a loose ball back into traffic queuing on the edge of the box.
The rapid exchange of first-time passes between Toornstra and Sam Larsson was top quality but there was little doubt Holland international Toornstra's strike was flying wide before it clipped Helander's knee to leave McGregor beaten.
Rangers looked relieved to get in at the break only one down, yet within seven minutes of the restart they were level.
Kent collected Steve Davis' pinpoint 40-yard pass before cutting inside Lutsharel Geertruida to deliver a cross which Morelos sent back across Marsman with a lethal nod of his head.
The Dutch hosts should have known better than to allow Morelos to drift in between centre-backs Botteghin and Marcos Senesi and they paid the price as the striker flicked another header into the top corner to put Rangers ahead after 65 minutes – his 24th goal in all competitions this season.
The Rangers faithful were in raptures, but their joy was curtailed just three minutes later as Sinisterra broke clear. Dancing one way then the other, he sat Helander on his backside before clipping his finish over McGregor.
Feyenoord were still bottom of the group and threw everything at Gerrard's men in search of an equaliser but they stood strong to ensure they remain the masters of their own destiny in two weeks' time.