Simon Clark’s men hit their visitors on the break so many times in the first half the game could have been dead and buried after 45 minutes.
As it was, goals from Matt Young and Leon Mettam gave the hosts a comfortable lead at the break, and a solid defensive performance in the second half sealed a £4,000 prize money windfall, and a first round proper tie at home to Kings Lynn Town.
When the full-time whistle went the home fans were jubilant, and Chester bewildered, having failed to score for the first time in 62 games.
Boss Clark was understandably thrilled with his squad, who made a side from the league above look very ordinary.
“I’m delighted, because we’ve done them over two games,” he said.
“Our game plan was to hold a line, which we did and I’m proud of them.”
“We trained hard for this game, our game plan was bang on, our energy and workrate were fantastic.”
And he sees the result, along with the performance, as a boost ahead of Saturday’s big league game at AFC Fylde.
“The players learned, from Monday’s training. And if players learn, we stand a right chance this season,” he said.
“If they can learn and do the things that work in a game plan, and win football games, that’s fantastic.”
The night didn’t start well for Tigers, left-back Owain Warlow pulling up with a tight hamstring in the warm-up, unable to start the game, so in came Stuart Ludlam.
But on just eight minutes, after a scrappy opening, Tigers found themselves a goal to the good.
Steve Towers fired in a great ball from the right, keeper John Danby denied Mettam twice but Young was there to fire home, under the stopper.
The first chance for the visitors was a snapshot from ex-Tiger Nathan Jarman that rolled harmlessly wide.
Then another lightning quick break had Chester all at sea, Lee Beeson playing in Mettam, the little striker going very wide to beat Danby but still managing to shoot back across goal into the far corner for 2-0 and a dream start for Worksop.
The tie should have been over on 24 minutes when Young sent Ash Burbeary clear and the forward tried an audacious chip with his left foot, Danby saving easily.
Seconds later Chester were split wide open again, this time Beeson getting clear and firing at goal, a touch from Danby taking the ball onto the bar.
As Tigers looked to break time after time, Paul Linwood was yellow carded for fouling Young, and the Worksop midfielder had a shot saved by Danby.
Mettam fizzed a shot just wide after a fantastic turn, and Towers had a decent effort saved.
Beeson’s inch perfect cross to the back post was nodded agonisingly over the bar by Burbeary, Worksop dominating their higher league opponents.
Wes Baynes’ crude challenge on Ludlam brought a yellow on 45 minutes, frustration showing for the visitors.
Seven minutes of the second half had elapsed before Chester, who made a double substitution at the break, had an effort on target, Jarman seeing his chip palmed over by Bastock.
Then a dangerous ball into the box found Jarman and he flashed a shot just wide.
Another yellow card was shown, this time to Antonio Sarcevic for his cynical foul on a breaking Burbeary, after a spell of Chester pressure.
And Dom Collins received a caution for his tackle from behind on Mettam, who had to leave the field for treatment.
Luke Shiels made an entrance on 67 minutes and made two fantastic interventions within a minute of replacing Beeson, the second to deny Tony Gray a shooting chance.
With a quarter of an hour left the ball dropped kindly for Craig Curran in the Tigers box and he hammered it into the side netting.
Worksop finally broke out from their own half, Burbeary setting up King and he went alone, his weak effort no problem for Danby.
Mettam industrious shift came to an end on 79 minutes, L’Heureux Menga taking his place and causing havoc for the Chester defenders, winning free-kicks, giving plenty away and earning yellow.
His cameo performance may not have caught the eye in terms of skill, but he kept Chester preoccupied and the last few minutes were almost exclusively played out near the corner flag in the Chester half.
The yellow card came out a few more times as Chester players grew increasingly agitated, before the whistle was greeted by rapturous applause from the Worksop faithful and Tigers marched on in the Trophy.
Worksop: Bastock 8, Clarke 9, Ludlam 8 (Wood 85), Young 8, Miller 8, HAWES 9, Beeson 8 (Shiels 67), Towers 8, Burbeary 8, Mettam 8 (Menga 79), King 8. Not used: Shiels, Telling.
Chester FC: Danby, Baynes, Clancy, Linwood, Collins, A. Williams (Gray 45), Hankin (Brown 54), Sarcevic, Jarman, Curran, Mackin (M. Williams 79). Not used: Horan, Howard.
Referee: R. Wigglesworth. Assistants: A. Hull, M. Tyers.
Goalscorers: Young 8, Mettam 17.
Yellows: Bastock 81, Menga 85; Linwood 28, Baynes 45, Sarcevic 60, Collins 62, Jarman 90, Brown 90.