The Gunners got both their goals in the second half as first Chambers and then Eddie Nketiah found the net.
Arsenal will find out on Saturday morning who they will face in the quarter-finals and Chambers believes Mikel Arteta’s side have what it takes to win the whole thing.
“We want to go all the way [now],” he said. “A club like Arsenal needs to be going all the way and competing for silverware in every competition, so that’s obviously our aim.
“That’s our goal, we’re fully focused on that and believe we can do that.”
Arteta made nine changes to his starting XI for the tie against Leeds, with only Ben White and Emile Smith Rowe keeping their places from Friday’s win over Aston Villa.
The pair would have been left out too, but an injury to Martin Odegaard and Pablo Mari being struck down by illness forced them to start.
White, however, was suffering with the same illness that kept Mari out of the squad and he had to come off after 55 minutes.
His replacement was Chambers, who immediately found the net with his first touch of the game as he headed home from a corner.
“All the guys on the bench who were putting me on, the set-piece coach Nico [Jover], the boss, they all said: ‘Go and score on your first touch’. So that was all that was in my head,” said Chambers.
“It was nice to see it come off my head and go over the line. It was definitely a first and a pretty unique way to score.”
Arsenal wrapped up the win 14 minutes later as Nketiah pounced on Liam Cooper’s poor header back to goalkeeper Illan Meslier to score.
The only concern for Arteta on an otherwise good night’s work was White going off due to illness and Kieran Tierney and Odegaard missing out on the squad due to injury.
Odegaard has been struggling after taking a knock to his shin last week, while Tierney has an ankle issue.
However, Arteta hopes that pair, plus White, will be available for Saturday’s trip to Leicester in the Premier League.
“They were both out with two different injuries,” said Arteta, when asked about Odegaard and Tierney.
“They tried on Monday but they didn’t feel great. They wanted to be involved, but they weren’t good enough to be selected. Hopefully in the next few days they can feel better and they can be available for Leicester.”
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