Story of the match
Wolves looked the more dangerous of the two sides inside the first five minutes, with their wingbacks Hugo Bueno and Nelson Semedo getting forward and causing Arsenal some problems in behind their defence.
The Gunners were dealt a major blow after just 15 minutes when Granit Xhaka, who has been integral to his sides success this season, was forced off the pitch with a suspected illness and replaced by Fabio Vieira.
Portuguese forward Goncalo Guedes had a great chance to give his side the lead after 20 minutes, being fed the ball by his fellow countryman Semedo, but his shot narrowly missed the target.
Arsenal striker Jesus came close again past the half hour mark, making a great run to latch onto good pass by Saka, but the 25-year-old snatched at the chance, curling the ball onto the crossbar.
William Saliba gifted Wolves a chance to take the lead on the cusp of half-time, with the Frenchman playing a sloppy back pass which was intercepted by Guedes, but the 25-year-old couldn't curve his shot on target from outside the box.
Both sides had good chances to take the lead in a very even first half, but the score remained level at the half-time break.
Arsenal captain Odegaard broke the deadlock 10 minutes into the second half, scoring from close range following a fantastic bit of buildup play by the Gunners, with Jesus poking the ball through to Vieira who dinked the ball into the box for the Norwegian midfielder.
Odegaard could have had a second but Wolves defender Toti Gomes did brilliantly to track back and intercept Jesus' pass to deny Arsenal of a good chance goal scoring chance.
The Gunners doubled their lead with 15 minutes left to play, and it was Odegaard who completed his brace. Gabriel Martinelli forced a good save out of Sa from the edge of the box, before the ball deflected back out to the Odegaard who belted the ball into the bottom corner on the half volley.
The home side nearly hit back with an instant reply as Daniel Podence threaded Guedes through on goal, but the Portuguese forward couldn't hit the target from a tough angle.
With five minutes to go Podence almost scored a wonder goal, flicking the ball up from a wayward cross and producing a bicycle kick which flew just past the wrong side of the far post.
Wolves couldn't trouble Arsenal in the closing moments of the game, as Arteta's men saw out a vital three points.
Both sides return to league action on Boxing Day, following the conclusion of the international break - Arsenal host West Ham at the Emirates Stadium whereas Wolves travel to Merseyside where they face Everton.