Sunderland goalkeeper Jordan Pickford made a string of brilliant saves to deny Arsenal before Sanchez broke the deadlock from close range.
Two goals from Alexis Sanchez inside the final 20 minutes saw the Gunners pick up a 2-0 win over Sunderland this evening, leaving them just a point adrift of the top four with one game remaining.
Arsenal now face the prospect of missing out on the Champions League altogether and will lose their place if Liverpool beat Middlesbrough at Anfield on the final day of the season.
And although Wenger tried to play down the importance of Champions League football, he said he is desperate to see Arsenal qualify for the competition this weekend.
Wenger's gamble paid off as Sanchez scored twice after the break to keep Arsenal's slim top-four hopes alive and the Gunners boss had nothing but praise for his star attacker after the final whistle.
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Thousands of fans stayed away, whether out of apathy or in response to calls from some fans to boycott the fixture as a show of dissatisfaction, with Emirates Stadium looking no more than three quarters full.
"I think nobody questions his desire and quality".
"We are in third position so it's in our hands", Guardiola, who will finish a season trophy-less as manager for the first time, said. "You would hope that every player would do that".
"We can talk and talk and talk, but let's make 75 points. if you look at the points we can make it's one of the best in the last 10 years". "You want all the teams to fight like Sunderland did tonight and, after, you have to accept the result". After that you deal with what happens, ' said Wenger after his team's 2-0 win over Sunderland last night.
"I'm surprised all of a sudden it becomes a big deal".
In the second-half, Arsenal upped the tempo, although Nacho Monreal nearly scored a freaky own-goal, an incident which would lead to an equally odd indirect free-kick for Sunderland deep inside the Gunners' box.