Lapses in Chester's defence coupled with clinical finishing from the Leeds line of attack ended the Blues' dreams of a Carling Cup first round success story in front of live television cameras.
Chester looked like they were heading for another heavy mauling on the back of their 6-0 drubbing at Dagenham and Redbridge at the weekend.
Jermaine Beckford completed a hat-trick after 34 minutes which was supplemented by other strikes from Robert Snodgrass and Andy Robinson as Leeds established a commanding 5-1 half-time lead.
But City looked a lot more assured and water-tight after the restart with Shaun Kelly replacing Paul Butler in defence, and Jay Harris substituting Richie Partridge in a five-man midfield as the Blues employed a 4-5-1 formation.
City boss Simon Davies made just two changes to the side that had slumped to a 6-0 setback in the capital on Saturday.
Skipper Paul Linwood had recovered from his back injury and started in place of Kevin Roberts, while midfielder David Mannix started in place of Harris.
The tie started disastrously for the Blues who trailed 2-0 inside the opening nine minutes.
A long punt upfield from Leeds' left back Alan Sheehan after just three minutes found Beckford whose first-time right-footed volley sailed beyond John Danby to find the bottom right corner of the net.
And a neat and tidy move in the ninth minute initiated from visiting keeper, Casper Ankergren, released Robinson who sprinted over the halfway line before feeding Fabian Delph, he threaded a pass inside for Snodgrass to rifle home.
City striker Kevin Ellison countered and forced Ankergren into a save after 14 minutes.
And Ryan Lowe pulled a goal back for the Blues a minute later after latching onto a pass from Richie Partridge and seeing his deflected shot from the edge of the box loop over Ankergren and drop into the net.
But Leeds inevitably regained their composure, rediscovered their crisp passing manouevres, and extended their lead with a stunning goal from Beckford in the 25th minute.
The striker controlling a loose ball with his right foot and lashing a powerful left-footed shot into the corner of the net.
It was all one-way traffic as Leeds dictated the tempo and took a stranglehold of the contest.
3-1 became 4-1 in the 31st minute courtesy of a sidefooted shot from Robinson after a one-two passing move crafted between Snodgrass and Beckford on the edge of the City box.
And Beckford wrapped up his flawless opening half performance in stylish fashion to make it 5-1 with a spectacular lob over Danby from 30 yards to find the top left corner of the net.
Chester made two changes at the break and switched to a more secure 4-5-1 formation in an attempt to reduce their rampant attack-minded visitors.
But Leeds could easily have increased their account after creating a succession of gilt-edged opportunities.
Visiting boss, Gary McAllister, made a triple substitution in the 52nd minute which saw Beckford replaced by Enoch Showmuni, Robinson replaced by Bradley Johnson, and Jonathan Howson replaced by Jonathan Douglas.
Luciano Becchio forced Danby into a tip-over save in the 56th minute, before Delph headed wide of the target, and Showmuni saw his six yard shot saved by Danby.
But Chester restored some respectability to the scoreline in the 74th minute when Ryan Lowe sent Ankergren the wrong way with his successful penalty kick, awarded after Mozika had been fouled.
Leeds looked content to run the clock down in the concluding stages, but there was still time to test the City backline.
Showmuni won the race for possession on the left wing, beating James Vaughan and Danby who completely bypassed the ball, but then recovered to clear the danger.
Showmuni then tried his luck with a stinging 25-yard strike which Danby had to gather at the second attempt.
But Chester certainly demonstrated some fight and battling qualities in a much-improved second half display.
Lowe created one last scoring chance two minutes into stoppage time when he raced to the right edge of the box and delivered a low cross to the back post where Ellison rifled a first-time shot into the sidenetting.
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