The Frenchman converted Ryan Giggs' hooked cross to end a disappointing run of results at Ewood Park for Sir Alex Ferguson's men.
Mark Hughes made one change to the side that lost 2-0 to Aston Villa last weekend. Brett Emerton returned in place of Michael Gray after a three-game lay-off through injury.
Ferguson named an unchanged side to the one that defeated Portsmouth 3-0 last time out in the league, with only Wayne Rooney and Ronaldo to keep their place in the starting line-up following the embarrassing midweek Carling Cup defeat to lowly Southend United.
In torrential conditions, both sides started slowly, with Saha registering the first effort at goal - a header over the bar on 10 minutes.
Rovers' best chance of the half came on 18 minutes when Shabani Nonda let fly from fully 30 yards. His powerful shot deflected off Nemanja Vidic and looked to be looping into the top corner of the goal, but it just cleared the bar.
From the resulting corner, Andre Ooijer headed just wide under pressure from Edwin Van der Sar.
United always looked in control and Rooney ought to have bagged a hat-trick before half-time. On 21 minutes, Giggs played in the England man down the left and, when Emerton slipped, Rooney closed in on Brad Friedel's goal, forcing the big American to save well at his near post with his legs.
On 33 minutes, Ronaldo galloped into space down the right, delivered a dangerous ball in across the face of goal, but the unmarked Rooney, who looked destined to tap home, got the ball stuck under his feet and David Bentley got back to clear.
Finally, two minutes before the break, the ball dropped to Saha on the edge of the area. The Frenchman turned and fired goalwards, Friedel could only parry low to his left, and Rooney somehow stroked the ball wide of the open net from six yards.
John O'Shea replaced the injured Gary Neville at half-time, but it was the visitors that made the immediate impact.
On 50 minutes, Patrice Evra was booked for a foul on Bentley, Morten Gamst Pedersen supplied a terrific in-swinging free-kick into the box and Zurab Khizanishvili's glancing header sailed inches wide of the far post.
And Rovers were left to rue the missed chance as United again moved up a gear. On 62 minutes, Rooney turned Ooijer inside and out before forcing a brilliant reaction save from Friedel, but just two minutes later the visitors took the lead.
Substitute O'Shea supplied a deep cross from the right, Bentley and Emerton stood still as Giggs hooked the ball back across goal and Saha was on hand to acrobatically steer home the winner.
Rovers had their chances late on, as Van der Sar was forced to punch clear under pressure from Benni McCarthy, before the big Dutch keeper was adjudged to have handled the ball outside the area and McCarthy was again thwarted after Tugay's sliced shot had dropped kindly to the South African six yards out.