Nottingham Forest leapfrogged Leeds shortly before kick-off with a 3-2 home win over Leicester and, while only goal difference separates the two sides, these are anxious times for Leeds fans.
Simon Grayson's side did most of the probing against the high-flying Royals, who travelled north harbouring hopes of automatic promotion, such is their confidence following their terrific surge up the table.
And while it took several superb saves from Reading goalkeeper Alex McCarthy to deny Leeds, the Yorkshire side have now won only one of their last seven league games, and both Hull and Burnley can now join them on 66 points if they win their games in hand on Saturday.
Grayson made four changes to the side held 2-2 by Watford on Saturday, with skipper Richard Naylor returning to the starting line-up for the first time since October and left-back Paul Connolly, on-loan Tottenham midfielder Jake Livermore and Billy Paynter also recalled.
Reading's Hal Robson-Kanu stepped in for the injured Jimmy Kebe and Noel Hunt was preferred to Mathieu Manset up front alongside leading goalscorer Shane Long.
Reading were denied an early lead when Leeds goalkeeper Kasper Schmeichel darted off his line to thwart Jobi McAnuff in the 11th minute.
Home fans had to wait until the 23rd minute before Leeds mustered their first effort on goal, Livermore weaving clear and crossing for Snodgrass, whose far post header was brilliantly pushed over the crossbar by McCarthy.
Livermore was then booked for his studs-up tackle on McAnuff and a tense first period was in short supply of anything more refined until Max Gradel snaffled the ball off Reading defender Zurab Khizanishvili and raced clear to fire a rising shot on target.
Gradel's strike had McCarthy in trouble and his fumbled save spun just the wrong side of the visiting goalkeeper's post.
Neil Kilkenny replaced Livermore at half-time and for the first 10 minutes of the second period the home side looked the more likely to break the deadlock.
Reading left-back Andy Griffin had the first real effort of the half though, cutting inside Gradel on the edge of the penalty area and firing into the side-netting.
Leeds were foiled by the woodwork soon after. Bradley Johnson's powerful run carried him through two tackles and into the box, but his left-footed shot clipped the crossbar.
Grayson sent on strikers Davide Somma and Sanchez Watt for Paynter and Howson with 10 minutes left and Reading manager Brian McDermott replaced Robson-Kanu with Manset.
Moments later Mikele Leigertwood flashed a 25-yard shot wide for the visitors.
Leeds broke forward in the 87th minute and after Gradel's shot was beaten out by McCarthy, the Ivorian winger crossed the rebound for Snodgrass and his header forced the visiting goalkeeper into another fine save.
Watt performed acrobatics to somehow get his shot away at the second attempt in the closing stages, but Leeds fell just short in their bid to head into the final three games of the season with destiny in their own hands.