Leading 2-0 thanks to Scott Arfield and Kemar Roofe goals, Benfica fought back to level thanks to goals from Goncalo Ramos and Pizzi.
From the side which defeated Aberdeen here at Ibrox on Sunday, boss Steven Gerrard made two changes, with Steven Davis and Glen Kamara coming in for Ryan Jack and Joe Aribo.
Between the sticks for Gers again was Allan McGregor – this being his 82nd match in European competition for the club – matching the record set by his former teammate Barry Ferguson.
Benfica enjoyed a lot of the early possession – but it was Gers who grabbed the lead after just seven minutes with a pretty crazy but altogether outstanding period of play.
It was Davis who started it all off with a super ball to Scott Arfield, who in-turn, sprayed it wide for Ryan Kent.
Kent skinned full-back Alejandro Grimaldo out on the right, and his cross evaded everyone in the area but it reached Borna Barisic to play a one-two with Morelos.
Barisic’s delivery met the head of Kemar Roofe, but somehow from close range, goalkeeper Helton Leite made a remarkable stop, but he could only palm it out to the incoming James Tavernier, who crashed a header off the bar.
Finally, however, it dropped for Arfield to rifle into the back of the net at the third attempt to hand the Light Blues a dream start and for him to grab his sixth of the season
Benfica looked dangerous, however, and neat footwork from Everton allowed him to get a shot away inside the area that went just over, while Leon Balogun made a super, last-ditch tackle to deny Rafa Silva getting a shot away.
Gers were quite happy to allow Benfica the ball, but they were doing superbly to keep them at bay, and went in 1-0 to the good at the break.
Into the second half, and Luca Waldschmidt shot wide at the front post in the opening minutes while at the other end, Gers screamed for a penalty when a Roofe cross appeared to hit the hand of Jan Vertonghen inside the area.
On 69 minutes, however, Gers made it 2-0 thanks to an absolute rocket of a strike from that man Roofe.
On the counter, a lovely backheel from Glen Kamara allowed Borna Barisic to drive forward and feed the attacker.
He kept driving to around 20 yards out, but rather than opting to slip Morelos in to his right, he arrowed an absolute thunderbolt into the top corner to put the Light Blues in dreamland with that being Roofe’s seventh Rangers goal.
Benfica weren’t finished, however, and on 78 minutes, they hit back – substitute Goncalo Ramos being on hand to beat McGregor from close range.
Gers almost hit back straight away – Leite tipping a Morelos strike onto the crossbar before Benfica cleared the danger before Roofe could follow up.
On 81 minutes, however Benfica were level. Pizzi showed neat footwork in the area to work an angle for a shot inside the area before rifling home past McGregor.
Gabriel had a dipping volley go just over for the visitors as they searched for a winner in the closing stages, while Kamara made a super tackle to prevent Ramos getting a strike away in the area.
Next up in the Europa League for Gers are Standard Liege next Thursday, where victory will take the Light Blues into the Last 32 with a game to spare.
RANGERS: McGregor; Tavernier, Goldson, Balogun, Barisic; Davis, Kamara, Arfield; Roofe, Kent, Morelos.
SUBS: McLaughlin, Ughelumba, Helander, Hagi, Itten, Barker, Stewart, Barjonas, Dickson, King.
BENFICA: Leite, Gilberto, Grimaldo, Vertonghen, Everton, Gabriel, Waldschmidt (Goncalves, 56), Seferovic, Chiquinho (Pizzi, 57), Silva, Jardel.
SUBS NOT USED: Svilar, Vlachodimos, Cervi, Bernardo, Araujo, Ferreira, Ramos, Ferro.
REFEREE: Radu Marian Petrescu