كتب : Hatem Maher
Walter Pandiani first-half hat-trick stunned the home crowd but Ruud van Nistelrooy's goal gave Los Meringues a lifeline.
Skipper Raul narrowed the gap shortly after the break and substitute Jose Reyes grabbed the equalizer three minutes before the hour mark.
Argentinean forward Higuain notched home one minute from time to lead Real to a precious win that put pressure on Barcelona, who face Real Betis later on Sunday.
The victory lifted Real to the league table's summit with 66 points, one ahead of second-placed Barcelona while UEFA Cup finalists Espanyol lie 11th on 45 points.
Former Deportivo La Coruna striker Pandiani put the visitors in front in the 15th minute when he connected with Rufete's cross at the far post to side-foot the ball past Ilker Casillas.
He doubled the lead in the 26th minute after he converted another fine cross from Rufete into the back of the net.
Dutch striker and Primera Liga's top scorer Van Nistelrooy pulled one back four minutes later through a close-range finish after being set-up by Roberto Carlos' flick-on.
Pandiani completed his hat-trick in the 24th minute after he was fed by Moroccan midfielder Moha inside the area before firing a shot that stuck the post and went into the net despite Real's appeal for offside.
Raul reduced the deficit four minutes after re-start when he chested Van Nistelrooy's superb back-heel pass before smashing home.
Spanish winger Reyes, who replaced right-back Cicinho, leveled the score eight minutes later following a defensive mix-up.
Higuain sealed the victory just before stoppage time when he steered home from a tight angle following a brilliant give-and-go with Reyes.