Harry Cornick put Town ahead five minutes into the second half with a superb finish into the top corner, before Stuart Dallas levelled for the hosts 13 minutes later.
Leeds were pushing for a winner, but the Hatters were excellent defensively with Simon Sluga making a number of saves throughout the 90 minutes, frustrating the league leaders.
Nathan Jones made five changes to the side that beat Swansea City 1-0 at the weekend, with Danny Hylton, James Bree, Ryan Tunnicliffe and Callum McManaman all featuring from the start, as well as Martin Cranie, who was drafted into the team just before the game as Glen Rea suffered an injury during the warm-up.
Shortly after McManaman picked up a yellow card inside the first minute for a late challenge, Patrick Bamford found space in the area but saw his effort from a tight angle saved by Simon Sluga.
There was a big shout for a Hatters penalty in the 15th minute when McManaman tangled with substitute Gaetano Berardi in the area, but referee John Brooks waved away the claims.
Whilst Leeds had the lion’s share of possession, the Hatters came close to opening the scoring minutes later when James Bree’s floated corner was met by Sonny Bradley, but Illan Meslier was able to block and clear for the hosts.
Kalvin Phillips tested Sluga from distance seven minutes before half-time, but the Croatian keeper smartly turned it behind for a corner.
Cornick replaced McManaman at half-time and made an instant impact with a superb strike five minutes after the restart. Tunnicliffe played an inch perfect ball through to the forward, who faced up Ben White, before curling a wonderful effort into the top corner.
Leeds were looking for a quick response after going behind and Sluga was forced into two saves in quick succession from Tyler Roberts and Jack Harrison.
Once more the keeper was tested, this time from Phillips’ free-kick and he recovered quickly to block Ezgjan Alioski’s rebound effort as well.
Despite his best efforts, Sluga was beaten in the 63rd minute when Dallas found the bottom corner to level proceedings.
Leeds were in the ascendancy after equalising and came close once more through Bamford, who hit the side netting with a first-time effort.
Pelly-Ruddock Mpanzu produced a teasing low cross into the box, but it was missed by everyone and cleared by the hosts as the game entered six minutes of added time.
The Hatters withstood late pressure from Leeds and the point gained at Elland Road means the Town are now within two points of safety as they remain unbeaten under Nathan Jones, and six games in total.
LEEDS: Meslier, Ayling, White, Cooper (Berardi 12, Alioski 45), Dallas (Shackleton 90+4); Phillips, Klich (Hernandez 61); Harrison, Roberts, Costa; Bamford.
Subs not used: Miazek, Douglas, Struijk, Shackleton, Gotts, Poveda.
Goals: Dallas (63)
TOWN: Sluga, Bree, Pearson, Bradley (C), Carter-Vickers, Potts, Cranie (Collins 64), Tunnicliffe, Mpanzu, McManaman (Cornick 45), Hylton (Bolton 64).
Subs not used: Shea, Lee, Shinnie, Moncur, Brown, Butterfield.
Yellows: McManaman, Carter-Vickers, Cornick, Potts, Collins
Goals: Cornick (50)
Referee: John Brooks
