Chambers opened the scoring in the 55th minute, 23 seconds after coming on as a substitute. The defender's header looked to have been saved by Illan Meslier but goal-line technology ruled that the ball had crossed the line.
"He totally deserved it," said Arsenal coach Mikel Arteta of Chambers' goal."It was a great moment because he helped us to win the game. He is someone who deserves the best, for how he is as a person and a professional."
The Gunners' second came in the 69th from a poor header back by Liam Cooper which left Meslier stranded as Nketiah rounded the keeper and his mis-hit shot from a tight angle just rolled into the corner.
"It's always nice to play, it's been a while, I have been working hard, waiting for my opportunity," Nketiah told Sky Sports.
The loss further adds woe to a Leeds side that has been struggling in league play.
"We conceded a goal, the goal that we conceded was at the start of the second half, after that the game wasn't the same," said Leeds manager Marcelo Bielsa.