Arteta, who was named on December 20 as the permanent replacement for fellow Spaniard Unai Emery, watched the team draw 1-1 against Bournemouth and lose 2-1 at home to Chelsea in his first two matches as coach, reports Efe news.
From the opening whistle of Wednesday's contest at the Emirates, Arsenal showed the same dynamism that was on display for the first half of last weekend's match against Chelsea
It took the Gunners only eight minutes to get on the board courtesy of club-record signing Nicolas Pepe, who hammered a Sead Kolasinac cross past United keeper David De Gea.
The Ivorian international, who came to Arsenal for a transfer fee of 72 million pounds ($95 million), had a chance to make it 2-0 in the 38th minute, but his shot hit the post.
The second goal came just four minutes later, however, and Pepe contributed, sending the ball to Alexandre Lacazette at the near post.
De Gea deflected the Frenchman's shot right to Arsenal defender Sokratis, who pushed the ball into the net.
Arsenal slowed down some after the break, largely ceding possession to the visitors, but while United threatened on several occasions, keeper Bernd Leno and the Gunners' back line proved equal to the task.
The victory only their second in 16 matches in all competitions brought Arsenal to 27 points, enough for 10th place in the Premier League.
Manchester United are fifth with 31 points whereas Man City trail second-place Leicester City by just a point. Everton sit in 11th place with 25 points.
( With inputs from IANS )