Chambers’ header crept over the line for the opener 10 minutes after the break, before former Leeds loanee Eddie Nketiah pounced to wrap up the tie.
The forward cleverly flicked the ball over a stranded Illan Meslier and just did enough to nudge it over the line before the visiting keeper could recover.
Leeds had looked the more threatening side until the first goal in an open and entertaining game against a much-changed Arsenal side at Emirates Stadium.
But Mikel Arteta’s outfit were comfortable after establishing their lead as the visitors became stretched looking for a way back into the game.
Arsenal, hoping to win the competition for first time since 1993, will find out their last-eight opponents in Saturday’s draw.
Gunners maintain unbeaten run
VAR may not have been in use but Arsenal’s opener still felt like it took an age to register as all eyes were fixed on referee Andre Marriner to see whether the ball had crossed the line.
The official glanced at his watch, gave the signal that Chambers’ header had squeezed in despite the best efforts of goalkeeper Meslier and the hosts’ delayed celebrations began.
Chambers ran to embrace Arsenal’s set-piece coach Nicolas Jover, who told the substitute he would score with his first touch of the ball while he was waiting to come on.
Jover was proved correct, just 23 seconds after Chambers entered the field as a replacement for £50m defender Ben White, who had limped off moments earlier.
Arteta said afterwards White was suffering from a bug, having been one of just two players to keep their place following Arsenal’s 3-1 win over Aston Villa last Friday, the other being the lively Emile Smith Rowe.
The Arsenal boss called on those coming into the starting XI to use their minutes wisely and young forward Nketiah did that by continuing his prolific form in the competition.
The 22-year-old has struggled for first-team opportunities but grabbed his seventh goal in eight EFL Cup appearances, two of those coming while on loan at Leeds, when he reacted to a mix up in the visitors’ defence to score the second.
Arteta has already tasted success at Arsenal, winning the FA Cup as a player and coach, and the recent signs are encouraging for the Spaniard as his side made it eight games without defeat.
Leeds have not won away against Arsenal since 2003 at Highbury and that wait goes on, but they were buoyed by a vocal travelling support and enjoyed the best of the first half.
Gunners goalkeeper Bernd Leno had to get down quickly to palm Jack Harrison’s fierce half-volley away and Daniel James proved a constant threat, but Bielsa’s focus now returns to the Premier League and a trip to Norwich City on Sunday.