The Magpies led inside three minutes as Gordon netted the club's quickest ever goal in the Champions League, racing onto Dan Burn's pass in behind the Qarabağ defence before cooly slotting the ball into the bottom left-hand corner.
The visitors doubled their lead after eight minutes through Malick Thiaw as the German defender rose from Kieran Trippier's inviting cross inside the box before heading the ball into the far left-hand corner.
Gordon extended Newcastle's advantage in the 32nd minute as the England international netted from the penalty spot, surpassing Alan Shearer as the club's all-time leading Champions League goalscorer in the process.
The Liverpool-born forward completed his hat-trick, a first of his senior career, two minutes later before netting his fourth goal of the evening, a second successful spot-kick, on the stroke of half-time.
Eddie Howe has made four changes to his starting XI as Nick Pope, Joe Willock, Anthony Elanga and Gordon all come in, with both sides competing in their first ever knockout fixture in the star-studded competition this evening.
Joelinton has been named in the matchday squad for the first time since suffering a groin injury in last month's Premier League visit of Aston Villa, with the Brazilian midfielder available to deploy from the substitutes' bench if required.
The Magpies, who finished in 12th place of the competition's League Phase, target a third consecutive away win in all competitions for the first time since January 2025 when facing the Azerbaijan Premier League champions at the Tofiq Bahramov Republican Stadium.
The play-off trip to Baku, totalling over 2,500 miles, is the longest-ever distance travelled by an English team in the competition's history but Newcastle are still set to be backed by 1,998 away fans.
**Newcastle United:** Nick Pope, Kieran Trippier (c), Lewis Hall, Sandro Tonali, Anthony Gordon, Harvey Barnes, Malick Thiaw, Anthony Elanga, Nick Woltemade, Joe Willock, Dan Burn.
**Subs not used:** John Ruddy, Aaron Ramsdale, Aidan Harris, Joelinton, Will Osula, Jacob Murphy, Alex Murphy, Jacob Ramsey, Leo Shahar, Sean Neave.