Antoine Semenyo put City ahead at St. James' Park, forcing Jérémy Doku's cross home from close range, before Rayan Cherki doubled their advantage in the tie deep into stoppage time.
United hit the woodwork and James Trafford made a magnificent save from Bruno Guimarães, both in a breathless, end-to-end second half, but it's still all to play for at the Etihad Stadium in next month's second leg.
After 16-year-old Joe Bartley had set the tone for a huge evening with a spine-tingling electric guitar performance of Local Hero on the pitch, to the backdrop of a stunning Wor Flags display in the stands, Yoane Wissa was presented with a great opportunity to open the scoring inside the opening five minutes.
Anthony Gordon spread play to Jacob Murphy on the right and the long-serving winger slid the ball in first time to Wissa. He steadied himself, but could only fire off target at the Leazes End.
Then an inswinging Gordon cross from the left was met by Joelinton, but the Brazilian couldn't direct his header towards goal.
Pope had been a virtual spectator in the first half but he had to be alert at the beginning of the second to prevent a ricochet off Gordon squirming over the line.
But Trafford made an even better save moments later when Gordon crosses and Wissa sent a looping header goalwards but the Manchester City goalkeeper tipped it onto the bar at full stretch. United kept the pressure on and Guimarães struck a post.
However, in the 53rd minute Semenyo struck his second goal in two matches since joining City from AFC Bournemouth. Bernardo Silva could only get a slight touch to Doku's left-wing cross but that fell perfectly for Semenyo to convert.
Guimarães tested Trafford with a low shot from range, but the goalkeeper gathered. Then a Lewis Hall corner caused chaos in the City box but Sven Botman and Guimarães were both unable to find the net.
The visitors looked to have made it two when Semenyo flicked home from a Tijjani Reijnders flag-kick but after a long, long VAR check, referee Chris Kavanagh went to the monitor and Erling Haaland was ruled offside.
That buoyed United and their supporters and substitute Sandro Tonali - on as part of a triple-change which also saw Anthony Elanga and Nick Woltemade introduced - flashed an effort wide.
In the 81st minute, Pope blocked a Cherki shot with his legs, then he got down well to deny the Frenchman in stoppage time. The home side, meanwhile, had some promising attacking opportunities, including a Barnes cross which the diving Woltemade came within a whisker of connecting with, but failed to create the big chance they needed to force an equaliser.
And Cherki swept Rayan Ait-Nouri's cutback beyond Pope in the eight minute of additional time to put City firmly in the driving seat. Down but not out, United travel to the Etihad Stadium for the second leg on Wednesday, 4th February.
Newcastle United: Nick Pope, Lewis Hall, Sven Botman, Joelinton, Yoane Wissa (Nick Woltemade 69), Anthony Gordon (Anthony Elanga 69), Malick Thiaw, Jacob Murphy (Harvey Barnes 45+1), Bruno Guimarães (c) (Kieran Trippier 87), Jacob Ramsey (Sandro Tonali 69), Lewis Miley
Subs not used: Aaron Ramsdale, Joe Willock, Alex Murphy, Sean Neave
