The first act of coach Mariano Garcia Remon, drafted in following the shock resignation of Jose Antonio Camacho on Monday, was to restore Beckham and Raul to the starting line-up.
There was little improvement but the night's one moment of brilliance, an exquisite Beckham free kick in the 61st minute, sent the side into provisional top spot in the Primera Liga.
"The team was under tremendous pressure," Beckham told reporters. "It wasn't a brilliant performance but it was important to get the result.
"We can take heart from the togetherness of the team."
A third 1-0 victory of the season gave Real nine points from four games and took them two points clear of a group of six teams who held the lead going into the midweek fixtures.
Among them are Espanyol, who are away at bottom club Getafe on Wednesday, champions Valencia, who travel to face Deportivo Coruna, and Barcelona, who are at home to Real Zaragoza on Thursday.
Camacho resigned after two defeats in four days, citing a lack of faith in his own ability to inspire any improvement in the side's poor performances so far this season.
Real ran out to whistles and boos from fans
A first touch of the ball for the Brazilian full-back led to ear-splitting whistles and Beckham, Luis Figo and Ronaldo were all jeered in the opening few minutes.
It was not until the 28th minute that Real created a chance, Luis Figo taking a nodded through ball from Morientes and slipping a shot wide.
Raul hit the post with a measured shot from the edge of the area and as the ball came back Albert Celades forced a fine one-handed save from keeper Ricardo Sanzol.
Sanzol reacted quickly again at the start of the second half to deflect Raul Bravo's flick from a near-post Beckham free kick.
Raul's sharp run down the left almost created a chance for Figo with 55 minutes gone and a few minutes later the captain's pass set Ronaldo up for a shot that flashed wide.
Real were still largely uninspired, though, and it needed a set-piece goal from Beckham, whipping in his free kick from a central position midway between the halfway line and the goal, to claim the points.
Osasuna had a couple of half-chances late on, and the crowd continued to voice their disapproval, but Raul was given a warm ovation when he went off a couple of minutes before the end in a sign that the fans may soon be willing to forgive and forget.