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The result extends Arsenal's winning run in the Premier League to five matches and they still have three games in hand on United.
The defeat leaves Leicester in 12th position in the league table as they set their sets on the Europa Conference League in midweek.
"We have a very strong belief in the group and play with a lot of confidence," Arsenal midfielder Martin Odegaard said.
"We just have to keep going. Everyone believes in what we are doing."
Arsenal started well and took an early lead after 11 minutes when Partey glanced home from Gabriel Martinelli's corner.
It was the 12th goal that Brendan Rodgers' side have conceded from a corner this season.
Partey almost grabbed his second seven minutes later but his effort from outside of the box crashed off the crossbar and away from danger.
The hosts were awarded a penalty after 59 minutes following a long VAR check as Caglar Soyuncu handled Partey's goalbound header off the line.
Lacazette stepped up and hammered the ball into the top corner from the spot to double Arsenal's lead.
The Gunners host second-placed Liverpool at the Emirates on Wednesday.