The stalemate, in front of Rovers' biggest home crowd of the season, stretched the home side's unbeaten run at Ewood to eight games.
United had the best of what few chances there were but Rovers were solid throughout and thoroughly deserved the point.
Defender Phil Jones, barely turned 18, produced a man-of-the-match show similar to that on his Premier League debut against Chelsea three weeks ago.
Rovers, who held Chelsea to a 1-1 draw that day, brought in Australian international midfielder Vince Grella for his first start since December in place of David Dunn, while teenager Jones continued to be preferred in central defence to club skipper Ryan Nelsen.
United, with their sights set on regaining top spot from Chelsea, made six changes from the side knocked out of the Champions League on away goals by Bayern Munich in midweek.
Federico Macheda lined up alongside Dimitar Berbatov in attack in place of the injured Wayne Rooney.
Blackburn had the first chance when a header from Chris Samba was collected at the foot of the left-hand post by Edwin van der Sar from a lofted through ball by Grella.
Paul Robinson in the Rovers goal was tested by a diagonal shot by Antonio Valencia following a neat one-two with Berbatov, while Gael Givet nipped in well to turn a cross from Ryan Giggs behind for a corner.
But Rovers refused to allow the champions to stamp their authority on the game.
On 34 minutes, Rovers suffered a blow when Samba had to go off through injury and was replaced by Nelsen.
A minute later, Nani shot wide for United after working his way past Morten Gamst Pedersen on the edge of the box.
The best chance of the first half fell just before the break to Valencia, who found himself one-on-one with Robinson racing into the penalty area, but the England keeper timed his advance perfectly to save with his legs.
At the start of the second half, Rovers sent on leading scorer Dunn in place of Brett Emerton as they looked to up the pressure on the champions.
United made a change of their own 12 minutes into the second half when Darron Gibson replaced Ryan Giggs in midfield.
A couple of minutes later, Nani fired a 25-yard free-kick over the bar.
Jones, having another splendid game for Rovers three weeks after making his Premier League debut against Chelsea, was on hand to brilliantly block a shot from Berbatov and Gibson put the rebound over the bar.
With 10 minutes to go, a long diagonal pass from Paul Scholes found Gary Neville racing into the area on the right and he crossed for Berbatov but the Bulgaria striker shot straight at Robinson.
Gary Neville put the ball wide for United in injury time as the visitors dropped two costly points on the road.