In contrast to Barcelona's dazzling 5-0 thrashing of Deportivo La Coruna on Saturday, Real were fortunate to survive two strong penalty claims as they laboured to a win that lifts them into second above Sevilla on goal difference.
"We scored three goals and got three points which is what we wanted," said Real boss Juande Ramos.
"Barcelona are playing magnificent football and that is why they are getting good results.
"We are not playing so well but are getting good results and wins give you confidence and the ability to play better."
Osasuna went ahead through Iranian international Javad Nekounam's 19th-minute header but gifted Real an equaliser early in the second half with goalkeeper Roberto allowing Sergio Ramos's tame shot to creep in.
Argentine Gonzalo Higuain struck his 12th goal of the season just after the hour mark to turn the game in Real's favour and Arjen Robben added a third they scarcely deserved.
Valencia lost ground on Real and Sevilla after falling to a 3-2 defeat at Athletic Bilbao.
Valencia twice took the lead but Fernando Llorente, recently capped by Spain, scored a 90th-minute penalty to win the game and Valencia are now four points behind second-placed Real.
Atletico Madrid failed to take full advantage of Valencia's slip drawing 1-1 at Almeria who played with ten men from the 53rd minute.
It was a match-up between two Mexican managers in Javier Aguirre and Hugo Sanchez - compatriots and long time friends - but there was no victor as Florent Sinama Pongolle cancelled out Kalu Uche's opener.
Atletico now sit sixth, three points off the Champions League places.
"We don't have as many points as we wanted at this stage but there is still the second half of the season to achieve our aims," said goalscorer Pongolle.
Real's preparations for the Osasuna match had been far from perfect with president Ramon Calderon resigning on Friday, creating more instability at the club who only axed coach Bernd Schuster before Christmas.
Real almost scored after 24 seconds with Higuain showing a great turn of pace to get into the penalty area only to have his shot saved.
Osasuna had almost beaten Barcelona last weekend - conceding two late goals to lose 3-2 - and took a 19th minute lead on Sunday when Jaroslav Plasil got down the byline and whipped in a great cross for Nekounam to head home.
It was the first goal Real had conceded since the 2-0 defeat to Barcelona in mid-December.
Ramos thought he had equalised in the 37th minute but the goal was ruled out for offside.
After the break the Spanish international got his goal with his speculative shot fumbled by keeper Roberto who allowed the ball to loop over his body.
Robben then set up Higuain for a simple tap-in and scored himself in the dying seconds.
Real had been let off the hook six minutes from time when Pepe appeared to foul Juanfran in the penalty area.
The referee waved away the appeals and Juanfran, already booked, was sent off for diving.
Osasuna coach Jose Antonio Camacho was livid and lashed out at referee Alfonso Perez Burrull.
"The whole world saw the penalty and he (Perez Burrull) did too because he signalled a penalty," fumed Camacho. "Referees make mistakes like everybody else but then he maintains this cocky attitude."
Villarreal ended a miserable run with a 2-0 triumph over Real Mallorca to rise to fifth, a point behind Valencia.
The club had taken one point from their last 12 before the Mallorca match but a Joan Capdevila strike and a Giuseppe Rossi penalty got them back on the winning trail.