The Town made it 12 home wins for the season to maintain their eight-point lead over Wycombe, who went second with their win at Kenilworth Road on Tuesday night, and ten-point advantage over fourth place with just under a third of the campaign to go.
Cornick struck his fifth goal of the season seven minutes before the break, although it could – and should – have been several more during a dominant display from Nathan Jones’ side against a promotion rival, who drop to sixth.
Jones made three changes, with two of his three deadline day signings making their debuts; Flynn Downes, who arrived on loan from Ipswich until the end of the season, and forward Jake Jervis, who signed late on Wednesday night from Plymouth Argyle for an undisclosed fee, coming into the starting line-up, with Lloyd Jones on the bench.
The other change saw Cornick return from the off, after appearing as a sub in midweek, while Danny Hylton was back on the bench after missing the last two matches with a hamstring injury.
With Rea playing centre-half and Flynn anchoring the midfield in a 4-3-3 formation that had Jervis and Cornick up front with James Collins, the Town started brightly.
Cornick collected a smart fifth-minute pass from Downes before turning to crack a 20-yard left-foot drive against the foot of the post, before Jervis carried the ball from deep inside his own half and letting fly with a 25-yarder that flew just wide.
Downes was impressing with his range of passing in the early stages – and continued right through to the end of a magnificent debut – but it was his fellow new-boy Jervis who was getting plenty of attempts in on goal.
The 26-year-old combined well with Dan Potts down the left in the 15th minute before sending a shot wide after the full-back’s cross was headed back into his path by Daniel Seaborne.
Four minutes later, Downes chipped a ball into the box looking for Collins, and centre-half Jordan Storey’s header went only as far as Jervis on the edge of the box, but he couldn’t keep his volley down.
Exeter had their first shot in the 20th minute, Hiram Boateng’s tame effort from distance saved comfortably, low to his left, by Stech.
Town were dominating possession and Stacey was making inroads down the right. It was from the former Grecian’s 27th-minute cross that Berry found space at the back post to fire a shot straight at Christy Pym in the Exeter goal.
Then, a minute later, Cornick’s slide-rule pass in to Collins had the striker looking to pick out Jervis in the six-yard box, but his cross was deflected onto the top of the crossbar and out for a corner.
Cornick was full of running, and after beating his man on halfway in the 32nd minute, he raced through the middle and had options either side of him, and maybe took the wrong one as he tried to slip Olly Lee in to his right, with Collins free and screaming for the ball to his left, and the promising move came to nothing.
Town were playing some excellent football, dominating the ball with the excellent Downes proving his Championship class as he dictated the play, and the deserved breakthrough came in the 38th minute when Berry fed Potts out on the left flank.
The full-back looked as if he was going to take Kane Wilson on to the byline, but instead drove inside the box and laid it back for Cornick to smash the ball into the top corner, with the aid of a deflection, from 18 yards to record his second goal against Exeter this term.
The lead might have been doubled within a minute, when Olly Lee let a 20-yard piledriver go, but Pym saved well, flying to his left.
It was a first half display that oozed class and control, without the conviction in front of goal that should have brought a second to make the half-time break a little more comfortable.
The Hatters came out after the interval in much the same mode they’d played for the first though – on the front foot.
After Pym had gathered a header from Collins, Sheehan played a ball down the left for Berry to nudge into Jervis’ path, but the ex-Plymouth man’s 20-yarder flew just wide of the visiting keeper’s left post.
Cornick was still revelling in the space given him down the right, and after trading passes with Stacey, the former Bournemouth flyer’s cross fizzed across the six-yard box, just ahead of Collins, and Wilson did well to clear just as Jervis was about to force it home.
In the 57th minute, the Hatters threatened again, Potts combining with Jervis to storm into the box, but his shot was deflected behind for a corner.
It was one-way traffic and Berry was the next to have a go, cutting in from the left only to see his 66th-minute shot go just past the post, before – completely unmarked – meeting a Sheehan corner two minutes later with a downward header that bounced up tamely into Pym’s arms.
At the other end, Sheehan and Glen Rea were comfortably nullifying the threat of Jayden Stockley, with Stech barely troubled between the Town sticks.
Jones made his first change in the 76th minute, bringing Hylton on for Jervis, who left the pitch to a deserved ovation – but predictably not as loud as the one reserved for the top scorer’s return from injury!
Hylton almost had an immediate impact, retrieving Cornick’s over-hit cross and nutmegging his man into Collins’ feet. The ex-Crawley striker spun and hit a shot on the turn that didn’t quite have enough curl on it to creep inside the far post.
Jones introduced his third new boy, namesake Lloyd Jones, in the 84th minute with Cornick – who had been a livewire all afternoon – forced off by a knock.
Straight after the restart following the substitution and Cornick’s treatment, Sheehan whipped in a right-wing corner that Hylton met with a header from two yards out, but couldn’t keep it down.
Exeter had the ball in the back of the net in the 87th minute, but the linesman had long since had his flag in the air for a foul on Stech, and the Town defence held firm against a volley of high balls into the box to see out the victory with a 15th league clean sheet in 31 games.
Next up is a trip to Stevenage, who were on the wrong end of one of the Hatters’ emphatic wins here earlier in the season, in a week's time.
This one might not have had the goals of that 7-1 – or the 8-2 or 7-0 – but the performance was just as impressive and another massive win secured in the bid to secure promotion to League One.
TOWN: Stech, Stacey, Rea, Sheehan (c), Potts, Downes, Berry, O Lee, Collins, Cornick (Jones 84), Jervis (Hylton 76). Subs: Justin, Shinnie, Mpanzu, D'Ath, Shea (GK)
Goal: Cornick 38
EXETER: Pym, Wilson, Storey, Seaborne (McAlinden 72), Moxey, Taylor ©, James (Holmes 55), Tillson, Edwards, Boateng, Stockley. Subs: Sweeney, Simpson, Jones (GK), Jay, Byrne.
REFEREE: Andy Woolmer
ATT: 8,788 (464 away)