The forward, brought on minutes before, picked out the top corner to secure all three points after Allan Campbell's earlier strike had been cancelled out by Teemu Pukki.
A first Boxing Day fixture for three years, Edwards made one change for his first home match in charge, an enforced one with the suspended Amari'i Bell replaced by Dan Potts - who was starting in the Sky Bet Championship for the first time since he was forced off through injury against Blackpool last month.
Carlton Morris scored the winner in the last meeting against the Canaries back in October and the former Norwich striker started up front again with Elijah Adebayo.
There was a single change amongst the substitutes, with Cauley Woodrow fit and returning to the matchday squad ahead of midfielder Louie Watson.
The Hatters began the game in positive style, Mpanzu and Doughty combining down the left to find Campbell in the box on six minutes, and his attempted curler was deflected past the far post.
Clark hooked a half-volley over the bar from the resulting corner, then the Town went even closer on ten minutes when Bree picked out Potts with a deep set piece delivery, but Adebayo couldn't divert the captain's header inside the post from close range after he had won the corner with a driving run into the City box.
Teemu Pukki soon flashed a 20-yarder over Horvath's bar at the other end, before Bree went closer still to opening the scoring, whipping a 25-yard free-kick - awarded for a high challenge on Clark - that Angus Gunn flew across his line to tip onto the crossbar, with Norwich's defence denying Morris the opportunity to profit on the follow-up.
The visitors reminded Town of their threat midway through the half when Gabriel Sara stung Horvath's palms from distance, before he skipped to the left byline and sent a low cross that eluded everyone in the Hatters' six-yard box.
The Hatters were playing well though, with Potts proving a threat at every set piece but heading wide when unmarked in the six-yard box, although the linesman's flag would have ruled it out.
Osho was unfortunate to receive a yellow card for a foul on Dimitris Giannoulis, for what appeared to be a fair challenge on the edge of the Norwich box, after referee Tim Robinson had ignored shouts for a penalty for handball against Andrew Omobamidele as the visiting centre-half mistimed his attempted header, before blocking Morris' shot.
Lockyer went into the book soon into the second half for a trip on Kenny McLean, who had been sent off for elbowing the Wales centre-half in the match at Carrow Road earlier in the season.
Adebayo was forced off by a knock just before the hour, with another former Norwich striker, Cameron Jerome coming on in his place.
Town made a deserved breakthrough in the 61st minute when Campbell robbed Giannoulis 30 yards from the Norwich goal and strode forward to fizz a beauty past Gunn, low into the corner of the Canaries net.
Horvath pawed a deflected McLean shot behind for a corner six minutes later, and Norwich were level on 69 minutes when Ben Gibson played a ball through for Pukki to fire an angled right-footed drive past the USA keeper.
Lockyer spurned two great chances to restore the lead with headers in the 74th minute, first sending Bree's left wing corner straight back to him when free in the six-yard box, then heading the return ball over the bar.
Isaac Hayden shot over for Norwich 76 minutes, and the Hatters were reduced to ten men with Osho shown a second yellow card with ten minutes to go for pulling back Pukki on the edge of the box.
While that yellow was warranted, huge question marks remained over the first five minutes before half-time, but thankfully Adam Idah blasted the resulting free-kick wide.
Undeterred, the Hatters pushed on and found a late winner through substitute Woodrow, who took a touch out of his feet and smashed the ball into the roof of the net.
There was further drama when Alfie Doughty headed clear off the line in added time to preserve the three points. The result was enough to move Edwards' side up to 12th place in the league ahead of an away trip to Queens Park Rangers in three days time.
Goals:
LT - Campbell (61), Woodrow (90)
NC - Pukki (69)
Att: 9,831 (1,039)