Joelinton, marking his 100th appearance in the English top-flight, sent the Magpies ahead at Carrow Road with a thunderous first-half effort before the Brazilian's tap-in six minutes later doubled his and United's advantage.
Bruno Guimarães' exquisite chip extended the Magpies' lead shortly after the restart, preserving back-to-back clean sheets in the process to complete a memorable afternoon in Norfolk and move into ninth place of the league table.
Eddie Howe made four changes to the side which claimed a 1-0 win over Crystal Palace on Wednesday night as club captain Jamaal Lascelles returned to the starting line-up along with midfield trio Sean Longstaff, Joe Willock and Jacob Murphy.
The Magpies created the opening goalscoring opportunity of the league encounter as Murphy, who joined the Magpies from Norwich in the summer of 2017, raced onto Guimarães' lofted pass but the winger's side-footed volley flew wide of the target.
Kieran Dowell went close to punishing Murphy's miss after latching onto Mathias Normann's dangerous pass in behind the United defence but lifted the ball over the target for the hosts.
Newcastle were fortunate to remain on level terms as Pierre Lees-Melou completed a mazy counter-attacking run before picking out Teemu Pukki and, after the Finnish forward rounded Martin Dúbravka, teed up Dowell who could only fire a wild effort over the crossbar.
Dan Burn went close to registering his first goal in Newcastle colours as the Geordie centre-back rose from Murphy's in-swinging corner before directing his header inches wide of the right-hand post.
However, in the 35th minute, Newcastle took the lead as Joelinton opened the scoring in terrific fashion.
After Emil Krafth and Jacob Murphy combined neatly down the right flank, the latter picked out Allan Saint-Maximin before the Frenchman's pass found its way to Joelinton, who lashed a fierce first-time effort into the net via the underside of the crossbar.
Newcastle doubled their lead before the half-time whistle as Guimarães threaded a neat through ball into Murphy's path who saw his shot deflect kindly into Joelinton's path, who calmly tucked the ball into an empty net.
Howe's side continued to push for a third goal before the break as Matt Targett's low drive was blocked by former Magpies goalkeeper Tim Krul before Sean Longstaff fired the rebound over the bar.
The Magpies continued where they had left off as, in the 49th minute, Guimarães netted his third goal in as many matches. As Krul attempted to play from the back, the Dutchman's pass was intercepted by the Brazilian, who cooly dinked the ball over the goalkeeper.
Dúbravka maintained Newcastle's healthy lead after keeping out Dowell's long-range free-kick, getting quickly across goal to turn the ball away from danger.
Joelinton went close to notching his first hat-trick as the 25-year-old picked the ball up on the edge of the penalty area before his powerful drive was held by Krul.
Pukki, who netted a hat-trick in a 3-1 victory over Newcastle in August 2019, went close to reducing Norwich's deficit as the striker was slipped through on goal before flashing a low effort wide of the far left-hand corner.
In the closing stages, Joe Willock almost added a fourth goal for Newcastle as the midfielder's deflected strike inside the penalty area was blocked by Krul's arm but it would not prove costly as Newcastle registered an away win at Norwich for the first time since January 1994.
Newcastle United: Martin Dúbravka, Emil Krafth, Jamaal Lascelles (c), Dan Burn, Matt Targett, Sean Longstaff, Bruno Guimarães (Dwight Gayle 87), Joe Willock, Joelinton (Miguel Almiron 67), Jacob Murphy (Matt Ritchie 74), Allan Saint-Maximin.
Subs not used: Karl Darlow, Javier Manquillo, Fabian Schär, Federico Fernández, Jonjo Shelvey, Chris Wood.
