The 16-year-old winger scored a magnificent individual goal 10 minutes from time as the 10-man Reds won 4-3 at Firhill Stadium.
It was a memorable return to Glasgow for Doak, who only joined Liverpool in a £600,000 move from Celtic this summer.
Doak set up Oakley Cannonier for Liverpool's opener before Rangers equalised through a Charlie Lindsay penalty.
The Merseyside club regained the lead through Melkamu Frauendorf and went further ahead when Cannonier scored his second of the match after again being set up by Doak.
Rangers were handed a route back into the game when Liverpool's Lee Jonas was sent off after the break. Arron Lyall pulled one back for the Scottish club before Robbie Ure grabbed an equaliser with around 20 minutes remaining.
But as Rangers pushed for victory, Doak produced a moment of magic to snatch all three points for Liverpool.
Collecting the ball near the corner flag, Doak twisted and turned before beating his man.
He then pushed into the Rangers area, working his way past several defenders before firing an unstoppable finish in the bottom corner with the outside of his boot.
Footage of his goal has gone viral on social media, with some Liverpool supporters keen to see the youngster promoted to the senior squad.
"Get him near the 1st team..and Cannonier," wrote one fan on Twitter.
YESSS Ben Doak!!— The Redmen TV (@TheRedmenTV) October 12, 2022
This is magical from the former Celtic teen against Rangers 🪄
Only 16 but potentially knocking on the door of senior recognition soon? 🚪pic.twitter.com/Jawg1oN4gn
Another added: "Would love to see him involved in the Carabao [Cup]."
While a third wrote: "Get him training with the big boys!"
Wednesday's victory was Liverpool's fourth straight win in this season's UEFA Youth Cup.
The Reds are currently top of their group on 12 points, five clear of closest rivals Ajax.
Featured Image Credit: BT Sport
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