The 24-year-old Norwegian struck after a quarter of an hour in the away meeting with Newcastle. From a position a few yards outside the penalty area, Ödergaard neatly thundered in the 1-0 goal with his left foot, his 15th Premier League strike this season.
Newcastle, who have three points to spare on table five Liverpool in the battle for the four coveted Champions League places, were far from harmless. Alexander Isak had a header at the post at the start of the second half but they never got any closer than that.
Instead, they were forced to watch as Gabriel Martinelli made his way down the left wing with 20 minutes left to play and sent in a low post that Fabian Schär unluckily steered into his own goal.
With the three-pointer, Arsenal continue to shadow Manchester City at the top of the table. One point separates the teams but then City have four games left to play while Arsenal only have three.