Sandro Tonali netted in the third minute to put United ahead on the night and extend their overall advantage in the tie. William Osula had seen his effort saved but Tonali was there to force the ball over the line at the Leazes End.
Then Joelinton volleyed home seconds later from Harvey Barnes' centre to make the lead even bigger for Eddie Howe's men, who now look certain - if they didn't already - to be in Friday's draw for the last 16, with a two-legged tie against either Barcelona or Chelsea in store.
Joelinton tried his luck again in the 17th minute but this time Mateusz Kochalski was equal to his effort.
The visitors, though, kept battling and Elvin Cafarguliyev forced a good save from Aaron Ramsdale in the 30th minute before the United keeper made an acrobatic intervention to tip Camilo Durán's shot over the bar.
In between times, Newcastle almost made it 3-0 in some style as Nick Woltemade spun and played in Jacob Murphy with one silky movement, but Murphy - on his 31st birthday - drilled wide.
Namesake Alex Murphy came from the start at St. James' Park for his full debut and his first outing in the Champions League as Howe made six changes to the side narrowly beaten at Manchester City at the weekend.
Early in the second half, Durán raced through to score for Qarabağ - sending the away fans wild and even earning a smattering of sporting applause from the Newcastle supporters.
But a couple of minutes later, the volume was altogether different when Sven Botman headed Trippier's right-wing corner beyond Kochalski to make it 3-1.
Botman came off almost immediately as part of a triple substitution, shortly before Dan Burn was penalised for a handball in the 56th minute.
Ramsdale saved Joni Montiel's spot-kick - but Elvin Cafarguliyev gobbled up the rebound.
Abdellah Zoubir then forced brilliant save from Ramsdale before at the other end, Kochalski denied Barnes twice, firstly after skipper Kevin Medina lost possession, then by holding a low strike from the winger.
There was a Newcastle debut late on for teenage full-back Leo Shahar; it was, therefore, a night to remember for him, and a satisfactory one for the Magpies.
**Newcastle United:** Aaron Ramsdale, Kieran Trippier (c) (Lewis Hall 54), Sven Botman (Joe Willock 54), Joelinton (Anthony Gordon 54), Sandro Tonali, Harvey Barnes, William Osula (Yoane Wissa 73), Jacob Murphy (Leo Shahar 87), Nick Woltemade, Dan Burn, Alex Murphy
**Subs not used:** Nick Pope, John Ruddy, Aidan Harris, Anthony Elanga, Sean Neave