The Gunners were frustrated by the excellent goalkeeping of Jordan Pickford until Sanchez capitalised with two goals in 10 second-half minutes.
Hector Bellerin and Granit Xhaka each fired over and wide, while Petr Cech denied Didier Ndong and Jermain Defoe at the other end, but Pickford stole the goalkeeping show, making 11 saves.
The 23-year-old thwarted Sanchez, Olivier Giroud, Aaron Ramsey, Danny Welbeck and Shkodran Mustafi, before the Chilean tapped in Mesut Ozil’s cutback on 72 minutes.
"It was a game we had absolutely to win. We did it, we have 72 points now and we have to focus to get 75"https://t.co/tV5DXXmF8g— Arsenal FC (@Arsenal) May 17, 2017
Sanchez scored an 81st-minute header when Pickford, for once, was foiled by Giroud’s hooked effort.
Arsenal move to within a point of fourth-placed Liverpool and remain three behind Manchester City, with one match, at home to Everton, remaining.
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