Arsène Wenger claimed Arsenal had to maintain their composure after being held for the majority of the game against Sunderland in midweek.
Arsenal were able to break the deadlock inside the 72nd minute through the in-form Sanchez. The Chilean was on hand at the far post to tap home from a pinpoint Mesut Özil cutback.
Sanchez then ended the game as a contest with another goal inside the 81st minute. After Sunderland 'keeper Jordan Pickford could only parry Olivier Giroud's effort toward goal, Sanchez once again found himself in the right place to head the ball into an empty net.
Arsenal are now on a three-match winning run in the Premier League.
Late but great from Sanchez
For long spells in the match, it seemed as if it would be one of those days for Arsenal, who despite having a significant amount of shots on goal, struggled to find a way past Pickford- who was in splendid form at The Emirates.
But Arsenal's man of the season, Alexis Sanchez, proved once again to be the difference for the north-Londoners. Having been a doubt heading into the game, his manager was delighted with his contribution, "with him, I feel he had something still left," said Arsene Wenger. "But once he’s on the pitch and gets the ball, he always becomes a devil and forgets his pain."
When quizzed on what turned out to be a timely win, the Arsenal boss stated;
"We were a bit frustrated at half-time because we missed many chances and overall it was important to keep our composure and not get frustrated. I believe we did that in the second half and in the end we won the game in a convincing way."
Final day showdown
Arsenal's victory against Sunderland means the race for the top four reaches its conclusion on the final day of the 2016/17 league campaign.
However, Arsenal will need a favour from recently relegated Middlesbrough, who are the visitors at Anfield in a clash against Liverpool.
Liverpool are currently a point ahead of Arsenal, with both teams having played the same amount of games, and a win against Middlesbrough will secure Champions League football for The Reds for next season, assuming Arsenal win their match against Everton.
22-year-oldcentre-backk Calum Chambers is currently on loan at Middlesbrough, which prompted questions on whether or not Wenger was hoping he could do his bit to shut Liverpool out. Wenger's response was; "of course, but we have first to do the job [against Everton]. We can get to 75 points, that would be four points more than last season.
"There’s a difficult patch we had and we played through periods in a very tough environment, I think the team has been very strong and responded very well."
Everything is in place for an exciting end to the season, will Liverpool see their job through? Or will Arsenal unexpectedly claim a place amongst Europe's elite in 2017/18? The answers to both questions will be revealed in due course.