Morris opened the scoring in the fourth minute, then restored it just 15 minutes in after City's Viktor Gyokeres had levelled, only for Gustavo Hamer to hit a stunning second equaliser just after the hour.
Captain Sonny Bradley returned to the heart of defence, slotting in alongside Gabe Osho and Dan Potts. Supplying the width was James Bree and Fred Onyedinma, the latter who making his first start of the season.
The midfield three of Allan Campbell, Jordan Clark and Luke Freeman remains, whilst Harry Cornick partners Carlton Morris up front.
Elijah Adebayo is amongst the subtitutes, so too is midfielder Henri Lansbury as the Hatters continue their search for a first home win of the season.
The visitors should have been in front inside the opening minute as Viktor Gyokeres raced onto a ball over the top but put his shot wide of the post as Ethan Horvath raced out to narrow the angle.
Within three minutes the Hatters had the lead and it was top scorer Morris who netted for the third home game in a row, blasting a right-footed shot past Sky Blues keeper Ben Wilson after Onyedinma laid Cornick's lofted cross into his path.
Gyokeres spurned another glorious chance to score with a free header straight at Horvath, before he did level in the 11th minute, racing onto a Ben Sheaf through ball and slotting past Horvath from just inside the box.
The Hatters regained the lead on the quarter-of-an-hour mark and once again it was that man Morris, taking a wonderful reverse pass from Cornick into the area and slipping a left-footed finish past Wilson into the bottom corner.
It was a breathless opening period with defences far from being on top of their game, but it was making for a thriller under the lights with Coventry justifiably feeling aggrieved at being behind, while the Hatters threatened every time they went forward too.
Onyedinma whipped one cross in from the left that had to be turned behind, then a flowing move down the same flank resulted in the wideman playing Freeman in to win a corner, which Potts almost forced in with his left foot after winning the initial header at the far post!
Onyedinma somehow found his way into referee Andy Davies' notepad for re-entering the play without permission after going off for treatment following a clash of heads with Matt Godden, and he continued to provide the Town's major threat with his tricky runs down the left.
Town almost had a third three minutes into added time at the end of the first half when Potts rose to meet a cross from James Bree, only for the post to deny him a second goal of the season, but Town were more than happy to head into the break with a lead.
Jones made a change at half-time, bringing Adebayo into the action in place of Cornick, but the Hatters had Horvath to thank for keeping the lead intact when Gyokeres drove in from the left flank to tee Jamie Allen up for a shot that the USA keeper flew to his left to tip over the bar.
Bradley did well to block a Gyokeres effort as Coventry threatened again on 58 minutes, and it was just after the hour that the visitors drew level again with a wonderful strike from Gustavo Hamer that gave Horvath no chance from fully 25 yards.
Onyedinma had the Town's first attempt of the second half with 72 minutes on the clock, but Coventry were well in the ascendancy and were soon threatening again at the other end, Sheaf unable to keep his shot down.
Jones brought Henri Lansbury and Amari'i Bell on for Freeman and Onyedinma, and with just under ten minutes to go Town had a huge appeal for a penalty turned down as Clark played a one-two with Adebayo and sent an effort curling towards goal, only for Kyle McFadzean to spread himself full length to block the shot, seemingly with his hand.
Ref Davies waved the Town appeals away, then Coventry survived the resulting corner as Potts headed towards goal, only to see the ball cleared off the line and eventually away from danger.
GOALS:
LT - Morris 4, 15
CC - Gyokeres 11, Hamer 61
ATT: 9,546 (1,028 away)
