Miguel Angel Nadal took charge of the team following Michael Laudrup's resignation in midweek and Hemed put Mallorca in front with a spot kick but Raul Garcia responded with two headed goals for Osasuna.
With 10 minutes to go Hemed kept his cool again from 12 yards to give Mallorca a point. Racing Santander drew 1-1 with Rayo Vallecano with Raul Tamudo scoring for the side from Madrid before Adrian Gonzalez equalised on the hour mark.
On Sunday, Barcelona travel to bottom of the table Sporting Gijon still looking for their first away win of the season in La Liga after draws against Real Sociedad and Valencia.
"To win the title you need to win a lot of matches away from home. We are now faced with another very difficult game and it is down to us to break this poor run," said Barcelona coach Pep Guardiola.
Real responded after picking up just one point from two games with a 6-2 win over Rayo Vallecano and then beat Ajax 3-0 in the Champions League.
They travel to Espanyol with Kaka restored to the starting eleven after a long battle with injury and loss of form.
"I feel a debt to the club for always having stood by me, it would have been easier to leave but I never considered that. I have the dream of triumphing at Madrid and I want to achieve it," said the Brazilian
AFP