It was young striker's first treble at this level as he made it seven goals in his last five reserve outings.
Eddie Silva Sousa and Mark Yeates with the goal of the night from 30 yards completed the goalscoring.
The result was never in doubt after three goals in a ruthless six-minute spell made it 4-0 at half-time following Tim Partridge's sending off for the home side.
It was a case of after the Lord Mayor's Show in the second half with the only real highlight Barnard's late tap in for his hat-trick.
Rob Burch made an important early save from Bjarni Gudjonsson before we started to click into gear midway through the first half.
Silva Sousa did well to set up Barnard in front of goal after 22 minutes only for Jonathan Tuffey in the City goal to dart out quickly and smother the chance.
There was nothing Tuffey could do though when the same pair combined two minutes later for the opener - Silva Sousa played it into Barnard and this time he finished well from 12 yards.
The game changed completely just 120 seconds after that with a somewhat controversial sending off.
Partridge slid in on Dilevski and he reacted by going face-to-face - not a head-butt, it has to be reported - and then there was a bust up between the pair that led to Dilevski being shown the yellow card and Partridge a straight red.
Manager Clive Allen later revealed that Dilevski had allegedly been struck but admitted, in other cases, the young Aussie might also have gone.
Nevertheless, once the game settled, we shifted gears spectacularly.
The second goal arrived via a mix-up between Craig Pead and Tuffey as the defender nodded the ball past his advancing keeper. The ball was rolling in for an own goal but Barnard wasn't to be denied, sprinted after it and slid to claim it before it went over the line.
That was 35 minutes and it was 3-0 seconds later with Yeates' beauty, a 30-yard strike that flew into the top left corner.
Three became four after 41 minutes as Philip Ifil sent in a devilish cross from the right flank that Silva Sousa finished with some aplomb.
Unfortunately, the goals dried up in the second half and the home side deserve credit for hitting back.
They created the better chances with Burch saving well from Gary McSheffrey and Stuart Giddings but there was no denying Barnard his hat-trick - the moment arrived two minutes from time as Michael Malcolm drove in a low cross from the right and Barnard tapped home from two yards.
24mins: GOAL. Good work from Silva Sousa to set up Lee Barnard who finished well from 12 yards. 1-0.
26mins: Partridge sent off after bust up with Dilevski, who reacted to initial tackle and perhaps lucky to only be showed yellow card.
35mins: GOAL. Defensive mix-up between Pead and goalkeeper Tuffey left Barnard with a race to the ball to claim a goal before it crossed the line for an own goal - he just made it. 2-0.
36mins: GOAL. Absolute cracker from Yeates into top corner from 30 yards. 3-0.
41mins: GOAL. Ifil superb low cross from right tapped in by Silva Sousa. 4-0.
Half-time: Coventry City 0, Spurs 4
88mins: GOAL. Malcolm latched onto O'Hara pass, low cross from byline tapped home by Barnard. 5-0.
Full-time: Coventry City 0, Spurs 5
Coventry: Tuffey, Partridge, Giddings, Pead, Bains, Deloumeaux, Gudjonsson, Wood, Suffo (Barry, 45), McSheffrey, Thornton. Unused subs: Belford, Reid, Hall,Wall.
Spurs: Burch, Ifil, Kelly, O'Donoghue, McKie, Hughes, Yeates, O'Hara, Dilevski (Maghoma, 59), Silva Sousa (Malcolm, 83), Barnard. Unused subs: Fulop, Defendi, Barcham.
Lee Barnard grabbed a hat-trick as our reserves took advantage of an early sending off to wrap up Wednesday night's clash against Coventry City by half-time at Nuneaton Borough.