An early Alfie Jones own goal was followed a minute before half-time by a fantastic first-half strike by Lansbury to secure victory against the Tigers, who had parted company with manager Shota Arveladze on the morning of the game and put former player and current first-team coach Andy Dawson placed in caretaker charge for the night.
Lansbury celebrated with a lawnmowing routine he has been waiting for over a year to reveal, this being the perfect way to open his account for the club since signing in the summer of 2021, as the Hatters moved into fifth place ahead of the rest of the weekend's fixtures.
Elijah Adebayo returned to the starting eleven as manager Nathan Jones made one change from the side that beat Blackburn in the game leading into the international break.
Last season's top scorer Adebayo replaces Cauley Woodrow, who started against Blackburn Rovers but was absent through injury picked up during training in midweek.
Allan Campbell started and in doing so made his 50th Luton appearance in midfield, alongside Henri Lansbury and Jordan Clark.
Reece Burke returned to his former club for the first time, whilst Amari'i Bell was fit and available having travelled away with Jamaica, playing against Argentina and the great Lionel Messi in the early hours of Wednesday morning in America.
Pelly-Ruddock Mpanzu was named in the first team matchday squad for the first time since April after building up his match fitness in two Development Squad matches during the international break.
The Hatters made the perfect start, taking a sixth-minute lead with a goal that had to be credited to Hull defender Jones, but owed everything to Adebayo's brilliance.
The striker was denied his first goal of the season as his instinctive volley from Lansbury's right-wing corner came down off the underside of the crossbar, with Jones unable to do anything other than turn it over his own goalline under pressure from Morris.
Captain Potts, making his 199th appearance for the club, might have doubled the lead but saw his header saved from a left wing corner delivered by James Bree, who then burst down the right to slide an inviting low cross into Morris' path, but the top scorer couldn't keep his 17th-minute effort down.
Hull came within a lick of paint of equalising in the 20tt minute when Regan Slater's 30-yarder deflected off the head of Potts and, like at the other end, bounced down off the underside of Ethan Horvath's bar, but was headed safely away by Reece Burke on his first return to the club he helped win promotion from League One two seasons ago.
Hull keeper Nathan Baxter had to push a free header from Morris, meeting another Bree set-piece, around the post on 39 minutes before the Hatters doubled their lead a minute before the break - and what a strike it was.
Baxter had already denied the Hatters once in the move, pushing Clark's shot away after Morris had picked out Adebayo with a cross from the left, but Bree put the ball back into the box and Lewie Coyle's header clear was returned with interest by Lansbury.
The midfielder struck the ball first-time on the half-volley from fully 30 yards, slightly to the left of the goal, with the bend from connecting with the outside of his right foot taking the ball well away from Baxter's reach and in off the far post.
It was the perfect way to open his account for the club, and the midfielder responded by revving up his lawnmower for a celebration to reflect his favourite pastime away from football - cutting his grass!
Jones was forced into his first change at the break, with Burke pulling up with an injury in time added on and needing to be replaced by Gabe Osho.
Hull made two changes on the hour, Cyrus Christie and Greg Docherty coming on for Dimitrios Pelkas and Oscar Estupinan, and within a minute Ryan Longman had sent a glancing header towards Horvath's goal after a decent spell of possession, but well off target.
The Town were soon asking questions at the other end again, Bree winning a free-kick just outside the area but unable to repeat his wonderful strike at the same end of the ground from earlier this year, his effort flying high over the bar.
Hull posed another question when Docherty crossed from the right for Ozan Tufan to meet the ball at the near post, but it appeared to hit his midriff and flew wide, then both sides had big appeals for a penalty turned down - Morris going down first with Jacob Greaves seemingly tugging his shirt, before Longman went down at the other end in similar circumstances with Lansbury. Referee James Linington remained unmoved on both.
Christie sent a curling effort over on 73 minutes and Jones was at full stretch to volley over, just before Jones made his next changes, bringing Mpanzu on in place of Lansbury for his first appearance after five months out recovering from a knee operation, and Cameron Jerome for Morris.
Osho almost caught out Baxter with a cross-shot from deep on the right, but there was little danger at the other end as the Town saw out a comfortable victory to keep their season revving into gear, with the grass looking much greener after recording back-to-back victories and a third in a row away from home.
Onto Tuesday and last season's play-off eliminators Huddersfield Town's visit to the Kenny!
Goals:
Jones (OG) 6', Lansbury 44'
Att: 15,730 (544 Hatters)