Sanchez opened the scoring on the hour at St Mary's before substitute Olivier Giroud made the game safe with a header seven minutes from time.

Victory took Arsene Wenger's side above Manchester United into fifth place in the table and left them three points below Manchester City, who occupy the fourth and final Champions League qualifying berth.

"We were focused and I felt that when we suffered, we stuck together," Arsenal manager Wenger told the BBC.

"We have another clean sheet and I know we can go forward and score goals. The whole team was dynamic, focused and showed a convincing desire to win the game."

Arsenal must now win their three remaining games and hope City or third-place Liverpool drop points if they are to secure a 20th successive season of Champions League football.

Having previously taken two points from a possible 24 in away games against current top-half teams, victory was a welcome tonic.

However, it came at the cost of an injury to Alex Oxlade-Chamberlain, who has found form in a new wing-back role.

"We don't know how bad it is," said Wenger. "It's a tight hamstring. We'll know more in the next 48 hours."

Arsenal went into the game on the back of a 2-0 win over Manchester United and procured the first sight of goal, with Aaron Ramsey firing wide after a foray by Oxlade-Chamberlain.

Saints had an opportunity to make the breakthrough when Arsenal's back three contrived to play both Dusan Tadic and Manolo Gabbiadini onside, but the latter's effort was repelled by visiting goalkeeper Petr Cech.

Oxlade-Chamberlain gave way in the 36th minute, with Hector Bellerin taking his place.

- Puel 'frustration' -

Gabbiadini curled a free-kick wide before Cech was called into action again, touching a powerful Nathan Redmond effort over the crossbar.

Sanchez had been quiet, but with 15 minutes on the clock in the second period he made the breakthrough.

Picked out by Mesut Ozil, he cut inside Saints centre-backs Maya Yoshida and Jack Stephens, leaving both on the deck, before finishing crisply.

Chile international Sanchez, 28, has now scored 20 goals in a league season for the first time in a career that has also featured spells with Udinese and Barcelona.

Giroud made sure of victory in the 83rd minute, nodding home after Ramsey had headed the ball across the box following more good work from Sanchez.

Arsenal saw out victory with little trouble to complete a first league win at Southampton since their famous 'Invincibles' season of 2003-04.

Southampton manager Claude Puel, whose side remain 10th, felt his players deserved to take more from the game.

"It's often the same against the big six," said the Frenchman.

"We cannot find a win. Every time we play good quality football with chances, but without the clinical edge and it's harsh on the players. 

"For me, we deserved minimum a draw and maybe a win. For them, in one situation, they scored. It's difficult to accept.

"It was interesting for many moments, but it's important to score. It's a shame and a big frustration. It was another game against a top-six side without reward."

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