Jose Mourinho's Real side seemed lost without inspirational top-scorer Cristiano Ronaldo, suspended for the game in Pamplona.
In a poor quality bad-tempered clash at the Reyno de Navarra stadium, the main incident came in the 76th minute when Kaka was shown a second yellow card for preventing Osasuna taking a quick free-kick.
The little-used Brazilian playmaker had been on the pitch for a little over a quarter-of-an-hour and was booked moments after coming off the bench for jumping with a flailing arm.
It was the 2007 World Player of the Year's first sending off at Real since he joined from AC Milan in 2009 and his first red card since he was dismissed playing for Brazil against the Ivory Coast at the 2010 World Cup.
Argentina forward Gonzalo Higuain had a frustrating game before being substituted, and even the introduction of Germany playmaker Mesut Ozil and France striker Karim Benzema in the second half failed to lift Real.
They dropped only 14 points in the whole of their triumphant 2011/12 campaign but have already drawn four games and lost four this term, while Barca have won all their matches except for a 2-2 draw at home to Real in October, when Ronaldo scored twice.
The Portuguese forward's absence was sorely felt, and Real have now failed to win the last three La Liga matches in which Ronaldo, who has scored 16 times this season, did not play.
Real defender Raul Albiol, handed a rare start at centre-back in the absence of the injured Pepe and the suspended Sergio Ramos, suggested the club had given up on their bid for a second successive domestic title.
"The league has to help us for the [King's] Cup and the Champions League," the Spain international said in an interview with television broadcaster Canal Plus.
"To build rhythm and get on a run of victories that will allow us to perform well in those competitions," he added.
"We have to find a positive dynamic, although it's clear that things are not going well in the league.
"We should have won. This is a tough stadium to play at and we suffered with a man down, but there is no excuse."
Osasuna's well-earned point lifted them off the bottom of the table thanks to a superior goal difference.
Two goals from captain Roberto Soldado secured three points for Valencia at their Mestalla stadium as the club continued to improve under new coach Ernesto Valverde.
Soldado bundled the ball over the line at a 50th-minute corner and nodded home a second goal from another corner a minute from time to kill off the game.
German midfielder Patrick Ebert produced a scintillating performance to lead Real Valladolid to a 3-1 win at home to Real Mallorca in the earlier kick-off that lifted Miroslav Djukic's side to 10th on 25 points.
Known as "the Kaiser" to home fans, Ebert got Valladolid's 21st-minute opener with a thumping long-range effort before setting up Oscar Gonzalez for their second in the 88th and the
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