Rangers' fate is in their own hands going into their final Europa League group game, following a 2-2 draw in Feyenoord.
Jens Toornstra gave the hosts a deserved lead after 33 minutes when his shot from just outside the box deflected off Filip Helander and beat Allan McGregor.
The Gers could consider themselves fortunate to go in only 1-0 down at half-time, but they equalised shortly after the break as Morelos guided the ball in from a delicious Ryan Kent cross (52).
The Colombian struck again after 65 minutes when he met Borna Barisic's ball to send Rangers into dreamland, but Luis Sinisterra responded just minutes later with a cool finish (68).
The result, coupled with Porto's 2-1 win against Young Boys, means Rangers are in a good position to qualify, with a win against the Swiss side on December 12 taking them through to the last 32.
Rangers fight back to earn priceless point
At half-time Rangers could have had no complaints if they were two or three goals behind after a first period which was completely dominated by the hosts.
Feyenoord: Marsman (6), Geertruida (7), Botteghin (6), Senesi (6), Malacia (7), Toornstra (7), Kokcu (6), Fer (7), Berghuis (8), Sinisterra (7), Larsson (6)
Subs: Narsingh (6), Ayoub (6)
Rangers: McGregor (7), Tavernier (6), Goldson (7), Helander (7), Barisic (6), Davis (6), Jack (7), Kamara (7), Ojo (6), Kent (7), Morelos (8)
Subs: Arfield (6)
Man of the match: Alfredo Morelos
McGregor pulled off a wonderful stop to deny Steven Berghuis from a corner after 19 minutes, and former Swansea midfielder Leroy Fer could only hit the post with a header from the rebound.
Sinisterra then blazed over from just yards out after a cutback from Lutsharel Geertruida's cut-back, and you started to wonder if the hosts were going to be made to pay for their early profligacy.
But they deservedly took the lead when Toornstra's strike from just outside the box took a deflection off Helander and beat McGregor.
After the break, Feyenoord continued to dominate, but Rangers stunned the home crowd with a goal out of the blue after Kent's ball was met by Morelos, who guided it into the left corner of the net.
Just over 10 minutes later and Morelos was on the scoresheet again, converting Barisic's delivery and sending Gers fans into ecstasy.
But Sinisterra made up for his first-half miss when he danced into the Rangers box and lifted the ball over McGregor to bring his side level.
At one stage it looked like a point would have been enough for Rangers to qualify, with Young Boys ahead against Porto, but two late goals from the Portuguese side mean Gerrard's side need a victory at home next month to qualify.
If they can repeat the performance from the second half, they should be playing knockout European football for the first time since 2011.
What the manager said
Rangers boss Steven Gerrard: "I think it's a fair result. Feyenoord were better in the first half, I thought we were excellent in the second. In patches of the first half I didn't recognise us - what we stand for, our identity, what we've worked ever so hard for.
"I thought we were passive at times - and slightly lucky not to be further behind at half-time. They got a bit of luck with the goal but Feyenoord certainly deserved to be in front at the break.
"I asked for the real Rangers in the second half and we got it. We're really pleased and proud of the boys to be in this position. Of course we would have liked to have got the job done today, but we can't control what happens elsewhere. This is a positive result even though you saw two sides of us today."
- Rangers have only lost one of their 16 away games across all competitions this season (W10 D5) and are unbeaten in six (W3 D3) since losing 2-1 to Young Boys in October.
- Rangers are winless in 15 away matches in all major European competitions (excluding qualifiers), drawing 10 and losing five since a 2-0 win at Sporting CP in the 2007-08 UEFA Cup quarter-final.
- Feyenoord are unbeaten in seven home European fixtures (including qualifiers), winning four and drawing three.
Rangers host Hearts on Sunday as they look to keep up the pace with Celtic at the top of the SPL. Feyenoord are at home to Zwolle in the Eredivisie on the same day.
The draw for the last 32 of the Europa League takes place on Monday December 16 in Nyon, with proceedings set to start at 12pm, UK time.