Harry Cornick's 12th goal of the season - and second winner as a game changer in South Wales - was enough to give the Hatters all three points and complete a perfect Easter on the Bank Holiday trip to Cardiff.
Cornick, on as a first-half replacement for the injured James Bree, headed the game's only goal in the 71st minute, one minute earlier than his match-winning strike along the M4 at Swansea in February, as Town took a giant step towards securing a place in the Championship play-offs.
Manager Nathan Jones made two changes. Following Sonny Bradley's dismissal against Nottingham Forest, Tom Lockyer came into defence, as did Dan Potts to replace Cornick.
Henri Lansbury was back amongst the substitutes after being forced off against Huddersfield, and Carlos Mendes Gomes was named in the matchday squad for the first time since facing Peterborough United earlier this month.
The Hatters were in the ascendancy from the kick-off, with Snodgrass at the heart of the opening two chances inside the first five minutes, first curling in a free-kick that Potts headed over, then sliding Oyedinma into the box, but his shot was just wide.
Captain Kal Naismith was soon trying his luck from distance, an eighth-minute shot that wouldn’t come down, before Cardiff registered their first attempt on goal ten minutes later, Rubin Colwill volleying Joel Bagan’s cross high over James Shea’s crossbar.
The hosts were forced into an early change, with Isaak Davies on in place of the injured Alfie Doughty by the 20-minute mark, and after Reece Burke had seen a header saved from a Snodgrass corner, Cardiff started to enjoy more possession without really creating a chance, Town blocking several shots and defending their penalty area well to limit the threat.
The Bluebirds' best chance came courtesy of an error from the Town, with Naismith's attempted pass to Burke on halfway catching Allan Campbell's ankle and rebounding into the path of Tommy Doyle, who played Jordan Hugill in for a chance that Shea raced off his line to save brilliantly.
In the few minutes leading up to half-time, however, the Hatters' injury curse struck again, first James Bree forced off and Harry Cornick on in his place, then Shea colliding with his own defender, Lockyer, and eventually having to be replaced by Harry Isted after attempting to carry on following a lengthy period of treatment.
For 25-year-old Isted it was a league debut, and fourth senior appearance having come on in the FA Cup fifth round tie against Chelsea last month when on-loan keeper Jed Steer suffered a serious achilles injury.
Cardiff had keeper Dillon Phillips to thank for keeping the scoresheet blank early in the second half when he pushed Snodgrass' effort away acrobatically, then Cornick sent a 55th-minute curler onto the roof of his net moments after Davies' had wasted the hosts' best opening from a counter attack at the other end.
A hat-trick of Hatters injuries was completed on the hour when Onyedinma limped off after racing to the byline, and hurdling over an innocuous-looking sliding challenge from Bagan, Peter Kioso coming on at right wing-back as the final game changer.
Kioso was at the heart of the Town's next opening, playing a one-two with Campbell and sending in a cross from the right that Cornick almost got something on at the near post, with Phillips eventually gathering off his own defender Perry Ng.
The breakthrough finally came in the 71st minute as Adebayo won a flick from Isted's long ball forward. Cardiff's defenders could only divert the danger out to the left, where Snodgrass took a touch and delivered an inch-perfect cross for Cornick to head into the top corner from ten yards out.
Isted was soon having to fall on a low snap-shot from Doyle, and he showed his composure to claim a handful of Cardiff crosses and relieve any pressure that might have been building, before racing off his line to gather at substitute Mark Harris' feet.
Despite the lengthening casualty list, the Hatters squad once again showed its strength in depth, and adversity, to manage the game out and bring another huge three points back over the Severn Bridge.
Goal:
Cornick 71