An already vociferous home crowd at RamsPark was given reason to erupt just three minutes into proceedings, when Mario Lemina slid the ball through for Osimhen to beat Nikita Haikin with a clinical finish.
The visitors continued to struggle against the intensity of Osimhen and their surroundings, with the striker getting his head on two Leroy Sané crosses but being denied by Haikin.
Bodo/Glimt eventually started to make forays forward of their own and had periods of possession that were met by whistles from the stands, although they still couldn’t test Uğurcan Cakır.
Osimhen offered a reminder of his threat as he pounced when Odin Bjortuft failed to convincingly deal with Ismail Jakobs’ cross, even if Haikin was equally alert to stop his attempt.
The goalkeeper was left completely helpless in the 33rd minute, though, as Osimhen accepted the gift of a lax Fredrik André Bjørkan backpass by rounding Haikin and sliding the ball into the empty net.
Chances did arrive at the other end before the break as Jens Petter Hauge fired wide after Roland Sallai had been dispossessed by Sondre Brunstad Fet, who then hit the post from range.
Kjetil Knutsen’s side continued to show intent after the restart, with Bjorkan embarking on an ambitious run before offloading the ball to Sondre Auklend, whose shot was blocked.
They were still given a huge warning moments later, when Osimhen and Yunus Akgun both passed up an opportunity to shoot before Sané was denied.
The visitors failed to heed it, though, and Haitam Aleesami was dispossessed by Osimhen on the edge of the box, setting up Akgun to beat Haikin at the second attempt.
Fredrik Sjovold was the next Bodo/Glimt player to gift Osimhen the ball, but retreated to block the striker’s second shot after his first had been saved.
The visitors finally got a goal of their own in the 76th minute with Andreas Helmersen heading in Bjorkan’s cross.
Even so, there was never any real doubt that Galatasaray would record the 21st win from their last 23 matches across all competitions, while continuing the emphatic response to their heavy defeat to Eintracht Frankfurt on the opening day of the UCL league phase.
They also ended Bodo/Glimt’s five-game unbeaten run in European league phase matches, leaving the Norwegian side on two points.
Flashscore Man of the Match: Victor Osimhen (Galatasaray)