After the moving pre-match tributes to the legendary Kevin Keegan - an iconic figure at both clubs - Lewis Hall blocked an early Florian Wirtz effort but barely four minutes in, United broke at pace, with Osula feeding Elanga.
The Swedish winger's low finish was unerring, beating Alisson in the Reds' goal and nestling in the bottom right-hand corner to give Matthias Jaissle and his side a stunning start in the German's first competitive game in charge of the Magpies.
Lukáš Horníček - one of three debutants in the Newcastle line-up, along with Amar Dedić and Sean Steur - got down well to deny Wirtz just after the 15-minute mark before palming away a dangerous Milos Kerkez cross as the visitors began to probe.
But the St. James' Park faithful were responding to their team's efforts and Osula's pace in behind gave him his first sight of goal, with Alisson smothering the shot before the rebound just eluded the United forward.
**Newcastle United:** Lukáš Horníček, Lewis Hall, Sven Botman, Yoane Wissa, Will Osula, Harvey Barnes, Malick Thiaw, Sean Steur, Anthony Elanga, Amar Dedić, Lewis Miley
**Substitutes:** Ewen Jaouen, Fabian Schär, Aladji Bamba, Bazoumana Touré, Jacob Murphy, Nick Woltemade, Joe Willock, Jacob Ramsey, Leo Shahar