Raheem Sterling opened the scoring with a delightful shot from the edge of the box in 14 minutes.
Arsenal pressed for a goal after the break, but Bernardo Silva passed on his hopes of a comeback with a 64-minute effort.
Starsport It brings you five things we learned about Emery's new side.
1) Arsenal tried a high pressure in the first half and tested City's ability to pass the ball from behind.
Pierre-Emerick Aubameyang led the attack with the support of Aaron Ramsey from midfield.
It worked to some extent in the first 45 minutes, but Arsenal started to falter after the break.
Emery has work to do if they are going to play a game of high pressure.
2) The defense is still a problem as City scored two avoidable goals.
Sterling was allowed to go from the left and groove home while Silva wandered through the box before putting Benjamin Mendy's cross into the house.
Sokratis Papastathopoulos is an improvement on the team's previous defenders, but Shkodran Mustafi remains a concern.
3) Emery is willing to give young people a chance.
The former PSG boss threw Matteo Guendouzi directly at the start of the XI, while Ainsley Maitland-Niles was cleared to fill the gap on the left side.
Arsenal needs to build thinking about the future if they are going to return to the first four and Emery should receive long-term support.
4) Arsenal needs to work on playing from behind.
Petr Cech, Sokratis and Mustafa did not seem comfortable with the ball at their feet under the pressure of players like Sergio Agüero.
City could have capitalized on several occasions, particularly in the first half, and it is questionable whether Arsenal has personnel to play a high-risk game.
5) Mesut Ozil disappeared again.
The former Germany international struggled to make a mark in Emery's first game in charge.
Arsenal needs more of its star man, especially with the powerful Aubameyang and Alexandre Lacazette who need a quality supply.
Arsenal will travel to Chelsea next Saturday.