Cornick opened the scoring with his second goal against the Latics in as many weeks, and was followed in the second half by Adebayo, who scored for the third successive match to move on to six for the season.
Manager Rob Edwards made three changes from last Saturday's league defeat against West Brom, with both Gabe Osho and Louie Watson keeping their places from Tuesday's FA Cup third round replay trip to the DW Stadium, with Alfie Doughty and Allan Campbell amongst the substitutes.
After an impressive cameo off the bench in the week, Cornick started up front alongside Adebayo, who had netted the 97th-minute winner in midweek after also registering against the Baggies.
Fred Onyedinma was in the matchday squad for the first time since October during the victory against Norwich City. The 26-year-old was amongst the seven substitutes, however as was the case on Tuesday, leading scorer Carlton Morris is absent due to injury, with Tuesday's opening goalscorer Cauley Woodrow joining him on the sidelines with a calf injury.
Town started brightly, and James Bree had already gone on a rampaging run down the right, cut short by a trip by James McClean that gave the right wing-back chance to whip a beautiful free-kick towards Adebayo at the far post, before Cornick opened the scoring on 11 minutes.
Attempting to play out from their own penalty area, Cornick pounced as Steven Caulker dwelt on the ball 18 yards out, then stood up to an attempted trip and fired past Amos with the aid of a deflection for his second goal of the season.
Then, on 21 minutes, a prolonged spell of Hatters possession ended with Mpanzu releasing Adebayo down the left, but the striker's effort from a tight angle as he drove into the Wigan six-yard box flashed across the face of Amos' goal.
Wigan had the ball in the back of the Town net in the 24th minute, but Ashley Fletcher's thumping header was ruled out by an offside flag, and although the hosts dominated possession for a 15-minute period, there was no threat to Horvath's goal until a volley from Fletcher that flew high over the bar two minutes before half-time.
Town came flying out of the traps again at the start of the second half, Cornick dispossessing McClean a minute in and pushing the overlapping Bree to the right byline, but Amos managed to claim his cross right off the head of Adebayo.
Horvath had to save a Fletcher shot low by his near post, but by the 52nd minute it two 2-0 with Cornick the provider this time, racing down the right and sliding Adebayo inside to finish with aplomb from the edge of the box.
Edwards made an immediate change, replacing Watson - who had turned in another impressive performance at the heart of the Town midfield - with Scotland international Campbell, and by the midway point in the half he had brought Burke on for Osho, and Doughty for Cornick as the Town boss refreshed the line-up.
Adebayo was booked by referee Andy Woolmer after a flare-up with McClean, who was also shown a yellow card and was soon being dispossessed by Clark, who teed Doughty up for a 20-yard shot that flew just the wrong side of the post.
Chances after that were few and far between, but after three meetings with Wigan in a fortnight, Town were happy to see out a second successive win at this stadium - and fifth in eight matches under Edwards - to send the 1,005 Hatters travelling happily back down the M6.
Goals:
Cornick 11, Adebayo 53
Att: 11,135 (1,005 Hatters)
