The visitors extended their unbeaten run against Leeds to nine matches, a sequence stretching back to early 2005, but will be disappointed to take only a point after creating the better chances.
Slovenian Milanic saw enough to encourage him after his first game at Brentford on Saturday ended in a disappointing 2-0 defeat, halting Leeds’ momentum following three wins and a draw under caretaker-boss Neil Redfearn.
The point gained lifted Leeds into the top half of the table, while Reading sit two places and a point above them in 10th.
Reading clearly enjoy playing at Elland Road – they won 4-2 there last March – and had striker Nick Blackman converted one of several clear-cut chances, the Berkshire club would have celebrated a fifth straight win against Leeds.
The home side began full of intent as they looked put to put Saturday’s defeat behind them.
But Blackman forced the first save of the game with a rising 25-yard shot that was turned over by home goalkeeper Marco Silvestri in the eighth minute.
Reading forward Simon Cox shot tamely at goal soon after and Silvestri was forced into a low, diving catch to intercept visiting skipper Chris Gunter’s cross as Reading settled into the game.
Leeds continued to probe patiently without causing Reading any undue alarm before being gifted a chance in the 37th minute when an errant pass from visiting centre-half Michael Hector found Alex Mowatt 20 yards out, but the home midfielder’s drive cleared the crossbar.
Guiseppe Bellusci then spurned Leeds’ best chance just before the break after Mowatt had been tripped on the edge of the penalty area, but the Italian defender blazed the subsequent free-kick high into the stands.
Reading looked the more incisive at the start of the second half, but both sides were struggling to carve out clear-cut chances and Milanic sent on substitute Luke Murphy for Lewis Cook in a bid to break the deadlock.
Oliver Norwood was orchestrating things for Reading from a deep-lying midfield role and his 66th-minute free-kick on the right edge of the area was deflected just over.
Visiting striker Glenn Murray’s header from Norwood’s resulting corner was blocked on the goalline by Silvestri to the relief of the home fans behind the Italian’s goal.
Rudy Austin was a 67th-minute replacement for Mowatt, while Reading boss Nigel Adkins swapped Cox for Hal Robson-Kanu soon after.
Austin’s right-footed free-kick curled over the crossbar with 13 minutes remaining and at the other end Blackman forced Silvestri to block his shot at the near post after being set up by Murray.
Both sides went for the winner. Leeds striker Billy Sharp’s low drive was saved by Reading goalkeeper Adam Federici and after five minutes of time added on, neither could break the deadlock.