The top scorer headed in his 16th goal of the season in the fourth minute as Town made it one defeat in 11 matches to cement themselves in fourth position in the Sky Bet Championship table, and firmly in the play-off spots.
Manager Rob Edwards made two changes, one enforced with Pelly-Ruddock Mpanzu having suffered an injury that forced him off in the 1-0 win at Sheffield United, meaning that Luke Berry - the man who replaced him in the first half at Bramall Lane - coming into the midfield from the start.
The other switch saw Alfie Doughty return to the starting XI after missing Saturday's victory through injury, with Fred Onyedinma moving to the bench.
The Hatters started the game in fourth place and on a run of just one defeat in ten league matches, the last four of which are unbeaten with three wins and a draw, while Bristol City kicked off in 13th, ten points adrift of the play-offs and 12 behind the Town, but they had an impressive record since the turn of the calendar year, with just one league defeat so far.
The Hatters made a dream start with a beautiful goal in the fourth minute, Morris hanging in the air to head Cody Drameh's brilliantly drilled cross from the right past Robins keeper Max O'Leary for his fifth goal in the last seven matches.
It should have been two on 11 minutes when Gabe Osho picked Elijah Adebayo out with another cracking ball from deep on the right, but as the Town striker chested down and shot past the advancing O'Leary, City defender Mark Sykes had got back on the goalline to clear.
Town were zipping the ball around on the greasy Kenny surface, rain teeming down from the Bedfordshire sky as Morris met another inviting cross from Leeds loanee Drameh, but couldn't keep this header down.
A rampant Adebayo did unbelievably well to stay on his feet when Cameron Pring was pulling him back as he raced clear onto a Morris pass in the 33rd minute, saving the City man from a certain red card if he'd gone down, but his shot was repelled by the chest of O'Leary, who then saved Berry's follow-up with his feet.
The next chance came on 38 minutes when Marvelous Nakamba, who was everywhere, shot over form the edge of the box after Morris had pressed O'Leary and Campbell had picked up the loose ball to feed the Zimbabwe international.
Bristol City hadn't registered a shot in the opening half, and had barely ventured into the Hatters' penalty area. They called Ethan Horvath into action within four minutes of the restart, however, Andi Weimann shooting low from 18 yards, only to find the American comfortably behind it.
Town were still asking all the questions, however, Berry's free-kick deflected behind for a corner after Campbell had been tripped on the edge of the area, a Doughty shot goiong the same way before O'Leary pulled off a terrific save to deny Morris a second goal from Osho's clever curling cross on the hour.
O'Leary made another good save from an angled Alfie Doughty drive before City boss Nigel Pearson made a double change, taking off top scorer Nahki Wells and Anis Mehmeti and replacing them with Sam Bell and Omar Taylor-Clarke.
Former Town striker Harry Cornick reminded the Kenny faithful of the threat he carried during the club's rise up the EFL prior to his January deadline day move when he swivelled and hit a shot straight at Horvath on 72 minutes.
City were awarded a free-kick 25 yards out for a foul by Bell on Cornick, when it appeared to be the other way around. Adebayo was booked for not retreating ten yards, but Alex Scott's effort was straight down Horvath's throat.
Morris was soon heading another Drameh cross inches wide with just under ten minutes to go, before Bell - who had turned in another excellent performance at left centre-half - had to go off with a knock, Reece Burke returning to action in his place.
Town had done enough to record another win and extend the advantage over the play-off chasers to seven points, folloing Norwich's draw at Huddersfield.
TOWN: Horvath; Drameh, Osho, Lockyer (C), Bell (Burke 87'), Doughty; Nakamba, Berry, Campbell; Morris, Adebayo (Woodrow 84).
Subs: Shea, Lansbury, Watson, Onyedinma, Taylor.
Goals: Morris 4'
ROBINS: O'Leary, Dasilva, Scott, Cornick, King, Mehmeti (Taylor-Clarke 63'), Weimann (C), Pring, Sykes, Wells (Bell 62'), Vyner.
Subs: Haikin (GK), Wilson, Tanner, Francois.
REFEREE: John Busby
ATT: 9,899 (858 away)
