It took the Gunners over 70 minutes to open the scoring. Sanchez got the first after Mesut Ozil half-volley cross found the Chilean to tap the ball home.
10 minutes later Sanchez headed in from three yards to mark his 23rd of the season.
It would have been far more comfortable if not for Sunderland ‘keeper Jordan Pickford.
The England youngster and likely target of Premier League clubs this summer made a number of top saves to keep his side in the game.
The Gunners have now closed the gap to Liverpool to just one point with one game remaining.
Arsene Wenger will be pleased with the victory. The Frenchman has now orchestrated seven wins in eight since switching to the 3-4-3 formation.
The Gunners go to Everton on the final day in an attempt to snatch 4th place. Liverpool have a home tie against Middlesborough.