The Royals have not won at the Madejski Stadium since beating Wolves back in January but dominated proceedings throughout on Saturday to leave manager Brendan Rodgers a frustrated figure.
Sullivan made a strong of saves to deny Rodgers a first home win as Reading boss and ensure that Sean O'Driscoll's side escaped with a point.
Rodgers handed debuts to Shaun Cummings, Brian Howard and Darren O'Dea while Billy Sharp was left on the bench for the visitors following his loan switch from Sheffield United.
Gylfi Sigurdsson had the first sight of goal with a long-range drive which sailed wide before his corner was headed by captain Alex Pearce straight at Sullivan in the Doncaster goal.
Sigurdsson - who celebrated his 20th birthday this week - was the standout player in the opening half hour and he nearly had the home side ahead midway through the half.
Jimmy Kebe's cross from the right was flicked on to Sigurdsson by Doncaster defender Adam Lockwood.
Sigurdsson rattled in a low shot which was well saved by Sullivan before the midfielder fired the rebound wide under pressure.
Howard went even closer minutes later when he almost scored a sensational debut goal.
The midfielder chanced his arm from 30 yards when he spotted
Sullivan marginally off his line and lofted a lob over the back-pedalling goalkeeper only to see the ball thump the top of the crossbar.
Reading goalkeeper Adam Federici then made a sharp save to stop Cummings from scoring in the wrong net as the half drew to a close.
Former Celtic skipper O'Dea was denied a debut goal after the break when Sullivan did well to palm his header away to safety before substitute Grzegorz Rasiak came close.
Howard slid a pass down the side of the Rovers defence and the Poland international fired in a low shot to the near post which Sullivan did superbly to keep out.
Doncaster captain Brian Stock then had a rare effort at the other end but pulled his effort wide before Sullivan ended the game in familiar style.
First he showed great reflexes to tip over a Pearce header and then got his fingertips to another header from substitute Kalifa Cisse to keep a clean sheet and earn his side a point.