Reds 3 (Hemmings 16, Jennings 63, 89)
It may have taken two attempts but Barnsley booked their place in Round Three of the FA Cup - a home tie with Championship Middlesbrough - after a comprehensive 3-0 at Chester.
After a relatively quiet opening it was the Reds who came close to breaking the deadlock through Luke Berry. Eleven minutes had passed when Hourihane's out-swinging corner eventually dropped to Luke Berry, and his vicious drive was blocked inside the six-yard box by Kay.
On 16 minutes the Reds took the lead and it was thanks to a fine finish by Hemmings. A free-kick in midfield found Berry, and after feeding Ramage, the defender's shot was blocked by Brown only for Hemmings to pounce on the rebound 12 yards out and hammer into the top corner.
Five minutes later, Dale Jennings should have doubled the Reds' lead after Devante Cole went on a good run. The Man City loanee found Jennings in the area and after coming onto his right foot, he curled wide of the post.
Kane Hemmings had a great opportunity to grab his second after taking his side on a lightning counter attack. As the defence opened up, Hemmings went for goal himself but Roberts appeared from nowhere to slide in before the striker could shoot on 33 minutes.
Jon Worsnop pulled or a brilliant, finger-tip save as Conor Hourihane took aim from 25 yards and the Chester 'keeper got across to his right to tip the ball past the post on 36 minutes.
From the resulting corner, Reece Brown eventually found the ball at his feet but he scooped over from 12 yards with just the goalkeeper to beat.
After Jennings' shot deflected and dipped up for Worsnop to save, Chester cleared for a corner - from which Luke Berry would be brought down in the box by Rooney. No penalty was given.
With just over 30 seconds gone in the second half, Dale Jennings jinked his way into the box from the left but could on drag a low attempt wide of the near post.
The hosts finally started to threaten after a quiet first half, but Mason Holgate prevented Chester from getting in at the far post as Kay's deep cross was well cleared by the youngster on 58 minutes.
Three minutes after the hour, Dale Jennings made amends for his earlier miss with a lovely finish to double his side's lead. Kane Hemmings kept a swift move from the right alive and found Jennings in the area - the winger swept a lovely first-time effort in low off the far post from 12 yards.
Craig Hobson glanced a header over Turnbull's baron 70 minutes as Turnbull continued to be untested throughout the night.
On 75 minutes again Hobson had a headed effort as he met Roberts' delivery from the left but he planted his header wide this time.
Former Barnsley man John Rooney tried his luck with two long-range drives that both sailed well over the bar as the clock ticked down.
The Reds made their first change on 84 minutes as Leroy Lita replaced Devante Cole in attack.
The game was wrapped up in fine fashion by Dale Jennings as he bagged his second goal of the night with a fine solo effort. He twisted and turned in the area before curling a low effort in the far post.
Hourihane charged forward in the first minute of three added on and his 25-yard drive was paired by Worsnop - Jennings pounced on the rebound and his hat-trick was almost sealed but for a wonderful reaction stop from Worsnop again.
Chester: Worsnop, Kay, Brown, Charnock, Roberts, James, Rooney, McConville, Mahon, Hobson (Winn 88), Heneghan (Greenop 67).
Subs: Roberts, Touray, Harrison, Greenop, Menagh, Blake.
Reds: Turnbull, Brown, Berry, Cranie, Hourihane, Hemmings, Jennings (Boakye-Yiadom 90), Ramage, Bailey (Digby 90), Holgate, Cole (Lita 84).
Subs: Davies, Treacy, Abbott, Cowgill.
Referee: Keith Hill