Both sides' defences were on top in a full-blooded encounter of few chances, with Reading closest to snatching all three points in the 87th minute when substitute Michail Antonio's angled shot from inside the penalty area hit the post.
But Leeds will also count themselves unlucky not to have grabbed a fifth away win in the Championship this season when skipper Jonny Howson's goalbound shot was brilliantly saved by Reading goalkeeper Adam Federici deep in stoppage time.
The Royals have now drawn their last four league matches, while Leeds stretched their unbeaten run to six games to hold on to their place in the top six.
Mikele Leigertwood made his debut for Reading after joining on loan this week from QPR and Zurab Khizanishvili returned to the starting line-up, while Leeds were unchanged from the side that drew at Norwich last Saturday.
There was little to separate the teams for the opening 20 minutes, with neither able to carve out an opening and it was a further 10 minutes before Leeds had the first shot on goal - Robert Snodgrass drilling in a free-kick from the edge of the penalty area.
Reading responded with a shot from Jem Karacan that flew over the crossbar and Noel Hunt's volley soon after was blocked by Leeds winger Max Gradel.
Khizanishvili went closest to breaking the first-half deadlock when Khizanishvili headed Jobi McAnuff's corner inches wide of the post five minutes before half-time.
Ian Harte was denied a goal against his former club when Leeds goalkeeper Kasper Schmeichel turned away his goalbound free-kick at full stretch five minutes after the restart.
Schmeichel was alert to Shane Long's header as Reading exerted pressure, but Gradel fired a warning for the visitors in the 54th minute when his shot from the edge of the area was held by Reading goalkeeper Adam Federici.
Jay Tabb replaced the injured Karacan and Jimmy Kebe was sent on for Simon Church as Reading manager Brendan Rodgers made a double substitution on the hour mark, but Leeds were proving dogged opponents and chances were still at a premium.
Long headed over the crossbar in the 70th minute before Leeds made two substitutions of their own with 15 minutes left, with strikers Billy Paynter and Ross McCormack sent on in a bid to snaffle a late winner.
Bradley Johnson threatened to do just that in the 85th minute, but headed the wrong side of the post.
At the other end Reading were denied a last-gasp win when Antonio, a 77th-minute replacement for debutant Leigertwood, fired an angled shot from 12 yards against the upright.
Hunt then fired a shot from the edge of the area straight at Schmeichel and Federici pulled off a superb save to keep out Howson's fine shot from the edge of the area in the 93rd minute.