It was a shocking mix-up between Czech goalkeeper Radek Cerny and Jamaican defender Damion Stewart that set the pattern for a miserable night for the Londoners.
There was no danger and no pressure as Stewart went to clear a long ball from Matt Mills in the 22nd minute and he headed back to where he thought his keeper was standing.
But Cerny had raced off his line to collect the ball himself and could only watch helplessly as it sailed passed him into the net.
It had been scrappy from both sides up to that stage although Doncaster tried to play some neat football despite the bumpy pitch.
Roving wing-back James Chambers almost put them in front in the 17th minute when he just failed to connect with a header in front of goal from a cross from Richie Wellens.
Cerny was stranded and had he managed to get something on the ball it would almost certainly have put Doncaster in front.
Samuel Di Carmine went close with a shot on the turn for Rangers and Stewart headed just wide following a corner before the own goal setback.
Doncaster gained confidence after that and they made it 2-0 in the 30th minute, when in-form striker Paul Heffernan headed home his fourth goal in six games after latching onto a flick from Sam Hird following a corner.
Heffernan was only inches away from adding a third a couple of minutes later and went close again in the second half.
Rangers battled all the way with Di Carmine having a fierce effort saved at full stretch by Neil Sullivan, but their miserable night was summed up when Dexter Blackstock fired high over the bar from close range.