A seventh clean sheet of the season came despite losing both skipper Sonny Bradley and then Tom Lockyer from the heart of defence through injury, with three full-backs finishing the game as the back three.
Manager Nathan Jones made three changes from the side that drew with Sunderland on Saturday, with Pelly-Ruddock Mpanzu making his first league start since April after he was a second-half substitute at the weekend.
Bradley returned to the starting line-up, joining Lockyer and Dan Potts in the heart of defence, with James Bree and Amari'i Bell occupying the width.
The third and final change came up front, with Harry Cornick brought into the attack ahead of top scorer Carlton Morris, who was named amongst the substitutes.
The Hatters started well, Bree getting on the end of a long ball down the right by Lockyer to cut a cross back from the byline for Cornick, who pulled his fourth-minute shot across the face of goal.
Town looked to get another shot on goal on 14 minutes when Alfie Doughty clipped a free-kick into the Reading box after he'd been fouled in the middle of their half. Bradley got the first contact, nodding down for Allan Campbell, but the Scottish midfielder appeared to be impeded as looked to get his shot off from just inside the area
Two minutes later Adebayo forced a save from Joe Lumley after racing clear of the Reading backline, before then teeing up Doughty for a shot from outside the penalty area, which the visiting keeper once again got down low to his right to save.
Campbell was booked midway through the half for a late challenge on Tom Ince, the former Hatters loanee returning to Kenilworth Road once more playing under his dad, former England international Paul, for a third different club.
Bradley's night was over in the 27th minute when he won a header, but was nudged by Yakou Meite in mid-air and landed awkwardly with his knee giving way. After a five-minute delay, the skipper was carried off on a stretcher with the home fans singing his name and he was taken up the tunnel.
Luke Berry came on in his place, slotting into his usual midfield role with Doughty moving to right wing-back and Bree to right-sided centre-half.
Ethan Horvath produced a brilliant save with his right hand in the 35th minute, diving low to push a Meite effort away after Reading had pounced on a loose pass as the Hatters tried to play out from their own box.
Andy Carroll had been kept fairly quiet up to the 43rd minute, when he rose highest at the far post to meet a cross from Amadou Mbengue, and although the former England striker connected cleanly enough, his header went down into the ground and the right side of Horvath's post as far as Hatters fans behind that goal in the Kenny End were concerned.
Reading continued to ask questions as half-time neared, Potts and Berry both producing brave blocks in five minutes of added time as Ince and Baba Rahman tried their luck from outside the penalty area.
Carroll had the first sight of goal in the second half, again rising for a trademark header from an Ince cross from the right, but again the ex-Newcastle man was off target.
A minute later Berry looked to be in through the centre of the penalty area, but he couldn't quite take Adebayo's pass in his path, then the latter drove across the Reading box, evading a couple of challenges after great work by Bree down the right, but Mpanzu's thunderbolt shot from Cornick's lay-off was blocked by the face of Rahman.
Just before the hour Town lost another centre-half when Lockyer had to go off, still apparently feeling the effects of a clash of heads with Carroll a few minutes earlier. Cameron Jerome was the man introduced in his place, to play up front with Adebayo as Doughty moved to left wing-back, Cornick to the right and Bell to left-sided centre-half.
Republic of Ireland midfielder Jeff Hendrick fired a 25-yarder just wide of Horvath's right post on 65 minutes, just before Meite went into referee John Brooks' book for a late challenge on Bell, who had tidied up brilliantly as the last man with the Royals looking to punish the Hatters on the counter.
Bell was soon setting Jerome away with a raking crossfield pass, but Reading managed to smuggle the ball away from Cornick as he tried to meet the veteran striker's centre at the near post.
Reading introduced another Irish international, Shane Long, to play up front alongside Carroll with Meite making way in the 73rd minute, but it was Ince who called Horvath into action once more with a dipping 30-yard volley that the American flew across his line to push away.
Jones made two changes of his own with 12 minutes left as top scorer Morris came on for Adebayo, with Luke Freeman replacing Campbell, who had run himself into the ground as usual in midfield.
Freeman tried an 80th-minute volley, but didn't quite connect, and although it deflected off a Reading head for a corner, the Royals defended it well and the Hatters were still without a clear-cut chance in the second half.
That would change in the 87th minute, after Yiadom had been booked for a foul on Morris, when Jerome nodded down into Potts' path, but the defender's right-footed volley flew just the wrong side of the post from 12 yards out.
Ince had another go with a minute left, Mpanzu blocking his 25-yarder, then Carroll headed a Tyrese Fornah cross across the face of goal and Fornah, the substitute, saw an effort from distance deflected over the bar in added time.
Neither side could find a way through, however, and had to settle for a point that keeps them level on 26 points just above mid-table, with the Hatters a place ahead in tenth on goal difference.
Att: 9,620 (926 away)
