Arsenal striker Danny Welbeck was delighted to score his fourth goal of an injury-ravaged season, despite his second-half header helping to down his former club Manchester United.
Victory moved the Gunners to within two points of their fifth-placed opponents and earned Arsene Wenger a first competitive win over Jose Mourinho.
Granit Xhaka, via a huge deflection, had opened the scoring for the home side, with Welbeck adding the second with a thumping header.
He told Sky Sports 1: "It was really important for us to get the victory today and obviously with our position in the table at the moment, we need to be further up there.
"It's something that we are all disappointed about but hopefully it will give us a good end to the season.
"I grew up there (United) so it's a special place in my life but once we get on that pitch it's just business at the end of the day and try and get the points for the team.
"When you score you've got to be happy haven't you? It's only normal."
Manchester United boss Jose Mourinho hailed the return of injured trio Chris Smalling, Phil Jones and Juan Mata, with the defensive duo lasting 90 minutes and playmaker Mata coming off with five minutes left.
"(Arsenal) had a bit of luck with their first goal," Mourinho said.
"I cannot demand any more from players who have played not one minute of football in the last seven weeks.
"I think Jones, Smalling and Mata were amazing the way they performed after seven weeks of being out."
Mourinho was also fulsome in his praise for young defender Axel Tuanzebe, who was handed his Premier League debut.
"I think he did an amazing job and I think Alexis (Sanchez) knows his name because the kid has played really well and other players were trying to do everything," the Portuguese added.
Wenger, who finally got the better of old adversary Mourinho in the Premier League, admits qualifying for the Champions League remains a long shot but said: "There's still a mathematical chance.
"We need some help but the best help we can get is from our own focus between now and the end of the season."