United's 10th consecutive league win, achieved despite a ragged performance, moved them to 62 points, eight ahead of second-placed Liverpool who face Manchester City on Sunday.
Nicolas Anelka marked the start of Dutch coach Guus Hiddink's spell in charge of Chelsea with the only goal in a 1-0 victory at Aston Villa. Chelsea moved above Villa into third spot but are a distant 10 points behind United.
Villa, who had last tasted a league defeat in November, were hoping to bolster their ambition of breaking the top-four monopoly with a win that would have knocked Chelsea out of contention, but were disappointing with their best effort being an Ashley Young free kick against the crossbar.
"We had good possession, good triangles and were dangerous in the box," Hiddink, who took over from the sacked Luiz Felipe Scolari until the end of the season, told Sky Sports.
"The only thing we didn't do was kill the game with the second goal and the second half we leaned back a little too much. But on the other hand we could have scored more."
Villa have 51 points, six more than fifth-placed Arsenal who gave a debut to record signing Andrei Arshavin in a disappointing 0-0 home draw with Sunderland. The Russian playmaker was substituted in the second half.
Stoke City drew 2-2 with relegation rivals Portsmouth while Middlesbrough remained in the bottom three after a 0-0 stalemate with Wigan Athletic. Bolton Wanderers boosted their survival hopes with a 2-1 defeat of West Ham.
RONALDO WINNER
United manager Alex Ferguson admitted his jittery side had been given a wake-up call by Rovers who were unlucky not to get a point after hitting the post and having a strong penalty claim turned down.
"We just deserved it, no more than just," Ferguson told Setanta Sport. "We gave away a bad goal and that was not indicative of our performances recently.
"They made it a real fight for us. This was a great lesson today, it just shows what this league is like."
United badly missed Edwin van der Sar in goal and Nemanja Vidic at the heart of their defence, both of whom were rested.
Rooney struck early with a close-range finish but Rovers stunned the Old Trafford crowd when Santa Cruz nudged the ball past keeper Tomasz Kuszczak and rolled it into the net from a tight angle.
United defender Jonny Evans had a headed goal unluckily disallowed by referee Howard Webb just before halftime while Rovers' Ryan Nelsen stabbed a shot against the post shortly after the interval.
United were not themselves, but Ronaldo can usually be relied upon to provide some inspiration and he did it again on the hour when he whipped a fierce free kick past the flailing arms of Rovers keeper Paul Robinson.
