The Portuguese attacker inspired his side to go goal crazy against Jose Luise Mendilibar's men who really struggled to compete with the stars of Madrid
The home side opened the scoring on 23 minutes minutes when Cristiano Ronaldo found the back of the net. Ibrahima Balde equalized eight minutes later before Pepe restored the lead on 34 minutes.
Higuain gave Madrid a 3-1 lead at the break before Ronaldo completed his hat trick early in the second period with two quick strikes as Osasuna were reduced to 10 when debutant Satrustegui was shown a second yellow. Karim Benzema added another two to complete the rout.
Jose Mourinho's men will remain as the league's leaders although rivals Barcelona can reduce the deficit to one point if they are victorious on Sunday evening versus Athletic Bilbao.
Despite looking a little casual in the early stages, Madrid took the lead in the 23rd minute through a slight defensive lapse from Osasuna. Angel Di Maria curled an inviting ball into the box from the right wing which was met with a precise header from Ronaldo, who diverted the ball over Andres.
The home team looked comfortable after going a goal up yet were pegged back on 31 minutes after a quick set piece from Osasuna. Madrid expected its opposition to shoot from the edge of the box until Raul Garcia quickly slid the ball to Ibrahima Balde who placed the ball between the legs of Iker Casillas and into the net from 12 yards out - amid complaints from Los Blancos players.
However, an angry Madrid did not have to wait long until they took the lead for a second time. Jose Luis Mendilibar's men failed to clear a corner which led to Di Maria whipping a cross to the back post which was headed into the bottom corner by Pepe, despite Ronaldo's best attempts to steal the goal.
Mourinho's men certainly had their tails up and added a delightful third on 40 minutes following some great build-up play. Mesut Ozil slid the ball to Di Maria on the edge of the box who then played a through ball to Gonzalo Higuain. The striker turned his marker before curling the ball into the top corner from 15 yards out - a wonderful goal from the in-form frontman, to give his side a comfortable half-time lead.
Madrid did not have to wait long in the second half to extend its lead when Satrustegui was shown a second yellow card in the 55th minute for bringing down Ozil in the box. Ronaldo stepped up to smash the ball into the bottom corner, sending Andres the wrong way.
Ronaldo grabbed his 12th Real Madrid hat trick three minutes later as Madrid scored its fifth of the game. Alvaro Arbeloa did well to make his way into the box before clipping a cross over to the Portuguese attacker to head into the top corner.
Madrid added another on 63 minutes when Fabio Coentrao beat Damia before clipping the ball into the box for substitute Karim Benzema to smash the ball past Andres from six yards out.
On 81 minutes the home side added a seventh goal after some good play by Arbeloa. The full-back won the ball in midfield before sliding it into the path of Benzema who lashed it home from 12 yards out past the helpless Andres to complete the scoring.
With an international break interrupting domestic fixtures next weekend, Madrid returns to La Liga action in a fortnight's time when it travels to Valencia. Osasuna will entertain Rayo Vallecano on November 20.