In a keenly-fought 200th league edition of one of English football's great fixtures, Arsenal went ahead in the 13th minute when Xhaka belted a shot from 30 metres out, with United keeper David de Gea seemingly wrong-footed by the curve of the ball.
"I made a mistake against Tottenham, looking down at the last moment, not watching (Spurs keeper Hugo) Lloris, but today I watched until the end, and being focused you score a penalty", the Gabonese striker told Sky Sports.
Leno's top class display against Man United on Sunday has significantly boosted Arsenal's chances of returning to the Champions League next season.
Solskjaer has turned the team's form around since taking over in December, following the sacking of Jose Mourinho. "We are really hungry", Aubameyang was quoted by the Independent.
Solskjaer admitted United's tame opening may have been in part caused by fatigue after their European heroics.
However, he has already served that two-game ban in the second leg against BATE, which Arsenal won 3-0, and the first leg against Rennes in his homeland last week. Sometimes it happens, we hit the woodwork twice.
Making it even sweeter, Arsenal climbed above United into fourth place in the race to qualify for next season's Champions League.
Arsenal boss Unai Emery was delighted with a statement result that showed his team can hold their own against the league's elite.
The Gunners are two points ahead of United and only one point behind third placed Tottenham, with sixth placed Chelsea three points adrift of the top four with a game in hand. We played well but they were always unsafe on the counter-attack and today with five at the back we were more compact. "The manager gave me the time and when I got the chance, I played good, so he said, "you will stay in goal".
"Being competitive like today for 90 minutes can give us a stronger mentality".