Adebayo saw a second-half penalty saved, but made sure of scoring for the fifth game in a row with an 88th-minute header to make it eight goals for the season as Town made it four matches unbeaten in all competitions.
Manager Rob Edwards handed Leeds loanee Cody Drameh a debut from the start against the side sitting one place above the drop zone, but with new manager Sabri Lamouchi in the dugout for the first time.
Right-back Drameh was ineligible for the Emirates FA Cup draw against Grimsby Town on Saturday, but was in from the off. Elsewhere in defence, Tom Lockyer captained the side alongside Reece Burke, in the absence of the injured Dan Potts.
Top scorer Carlton Morris made his first start in four matches, partnering Elijah Adebayo up front, while new signing Jack Walton was amongst the substitutes along with Fred Onyedinma, who made his first appearance in more than three months at the weekend.
Town started well, Pelly-Ruddock Mpanzu seeing a shot blocked from the edge of the box and Drameh looking lively down the right before Cardiff fired two warning shots in the eighth minute, Sheyi Ojo shooting straight at Ethan Horvath before Callum Robinson hit a 25-yarder that skimmed the top of the crossbar.
Ojo tested Horvath again on 15 minutes, though the USA keeper was comfortably behind it at his near post.
Town were asking questions of their own, however, with the threat coming initially down the right with Drameh - who survived one attempt to pull him back by Jack Simpson to put a dangerous ball across the six-yard box - and Woodrow, dug a deep cross out that Adebayo met with a towering 27th-minute header, saved by Ryan Allsop.
Mpanzu and Amari'i Bell then combined on the left for the latter to whip in an inviting cross, which Mark McGuinness did well to head behind as Adebayo readied himself to pounce at the far post.
The Hatters came flying out of the blocks after half-time, Drameh playing the ball inside for Woodrow to bend one just over the bar, then Ojo hit a free-kick at the other end that flew over the frame of Horvath's goal.
Mpanzu did well to beat his man by the left corner flag and deliver a low ball into the six-yard box, but McGuinness again was on his mettle to lift it over his own bar and clear the danger.
Ojo was proving Cardiff's main threat, and the right winger brought a flying save out of Horvath just after the hour, but Drameh and Adebayo soon combined down the Hatters' right, with the latter fizzing a low cross towards strike partner Morris, who couldn't quite connect at the near post.
With just over 20 minutes to go, Edwards made his first changes with Onyedinma coming on for Drameh and Luke Berry for Woodrow.
Within seconds, the Town had a chance to make the breakthrough when ref Geoff Eltringham pointed to the spot for handball against Cedric Kipre as Adebayo looked to lift the ball over him in the box. The Town man saw his spot-kick saved, however, as Allsop dived to his right to push his low shot away.
Ryan Wintle spurned a clear-cut chance for Cardiff when Robinson floated a ball over the top for him to volley at goal, but he sliced his effort well wide from the edge of the box.
Onyedinma was flying down the right, firing three beautiful crosses in that begged to be finished, with Doughty smashing the middle one first time on the volley, but off target.
The breakthrough finally came in the 88th minute when Doughty crossed and Adebayo rose highest to head past Allsop and set the Kenny alight.
Goal: Adebayo 88
Att: 9,031 (544 away)