Arsenal scored a solitary goal against West Ham to go five points behind Chelsea who currently hold the fourth position.
Lacazette scored the only game of the day with only 12 minutes to the end of the normal 90.
The French forward completed a perfect setup from Mezut Ozil before it was ruled out for an offside.
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A VAR decision was called in before it confirmed that it was indeed an onside assit thus stood as a goal.
It was the third straight win for Arsenal at home, the first one since the month of February 2020.
David Moyes side seemed optimistic of scoring a goal but the win extended their away loss to six games.
Speaking following the win, Mikel Arteta praised his boys saying that big teams always find a way of winning big crucial matches.
He continued by admitting there was a long way to go but noted how the Gunners were taking shape to becoming the club that many expect much from.
Why Arsenal still needs major improvement
Even though the goal and win was crucial, Arsenal was exposed to still have weeknesses that need to be dealt with.
Throughout the match, there was lack of leadership and aggressiveness to score as many goals as possible.
They also lacked the pace to drive the ball upfront and take advantage of West Ham defense errors.