Bukayo Saka's first half goal was enough to give us all three points at Villa Park and strengthen our hold on fourth place.
It was a very professional performance from start to finish, restricting Villa to just one shot on target - which was in fact the last kick of the game.
We started the game very strongly too, playing mostly in the Villa half, and creating a few early chances.
Bukayo Saka was coming out on top of his duel with Ashley Young, and his cross in the first ten minutes was nearly turned in for an own goal by Ezri Konsa, but former Gunner Emiliano Martinez got down to make the save.
Emile Smith Rowe, back in the side for Gabriel Martinelli who's suffering with illness, shot over from the edge of the area from Martin Odegaard's pass.
But just before the half hour we scored the goal that our start merited. A quick free kick on the right was played to Cedric. His deep cross was cleared to the edge of the area, where Saka smashed the ball back through a crowded area and beyond Martinez.
It was the 2,000th goal Arsenal have scored in Premier League history, and Saka's 10th in all competitions this season.
Saka was on the receiving end of a late Tyrone Mings challenge shortly afterwards, and the Villa captain was perhaps lucky to stay on the pitch.
Bernd Leno, in for the injured Aaron Ramsdale didn't have a shot to save in the first half, on his first Premier League appearance since August.
In fact there was an hour on the clock before the hosts had a shot of any type - John McGinn curled one just wide from 20 yards.
There were signs though, that Villa were growing into the game slowly. Douglas Luiz fired a free-kick over the bar and Ollie Watkins hit the base of the post with a deflected shot.
Arsenal meanwhile, were looking to take the sting out of the game and keep possession in midfield. One such passage of possession play led to a chance for Lacazette on the edge of the area, but his shot was blocked.
Danny Ings, on as a late substitute, looped a header over late on as Villa piled on more pressure.
Coutinho had a free-kick deep into injury time pushed away by Leno, and the visiting fans could celebrate at the final whistle.
WHAT IT MEANS
After the international break we'll return to action in the Premier League away to Crystal Palace, on Monday, April 4.
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