Madrid trailed three times in the match and also had Sergio Ramos sent off just before half-time, but the champions managed to overcome those problems and claim a thrilling 4-3 win.
Higuain was his side’s hero with all four goals, but the Argentinian was keen to share the plaudits around, praising both his teammates and the Madrid fans at the Bernabeu.
“The team showed courage throughout the entire match and that’s why we won,” said Higuain.
“It’s important to excite the fans and make them support us like they did. It’s good to try to get them going sometimes.
“They were great today and I’m glad we were able to pay them back with a victory.”
The 44th-minute dismissal of Ramos could have proved a major setback for Real, with the Spain full-back shown a straight red card after the referee felt he had deliberately stood on the chest of an opponent.
However, Schuster felt that sending-off, plus the second-half penalty awarded to Malaga following a challenge by Fernando Gago on Duda, actually helped inspire his side.
“The penalty and Ramos’ red card made us stronger,” said the German.
“We proved we can grow stronger against adversity last year. We are the only team capable of this, but I would prefer to win some other way.
“Victories like this boost our morale and we have to try to improve on our mistakes in our next fixtures.
“We hardly have time to work in our training sessions, but this victory has made the team psychologically stronger.”
Elsewhere, Samuel Eto’o struck four first-half goals as Barcelona thrashed Real Valladolid 6-0 at the Nou Camp.
Barca’s eighth straight league win gives them 25 points from 10 games, one ahead of Villarreal in second and two ahead of champions Real Madrid in third. The Cameroon striker fired a brilliant quadruple in the first half to set Barcelona on their way to an eighth successive Primera Liga victory.
Eto’o opened the scoring after 12 minutes, adding a second on the half-hour mark and completing his hat-trick in the lead-up to half-time.
The African striker then added a fourth goal a minute before the interval to round off a superb first half for the Catalan side. Eidur Gudjohnsen and Thierry Henry also netted late on to complete the rout.
Last night Villarreal climbed to second after a 2-1 home win against Almeria. Giuseppe Rossi and Joseba Llorente got the goals for the home side.
Valencia climbed to third after a 3-0 win away to Getafe thanks to Fernandes, Joaquín and Rodríguez.
Elsewhere, Frederic Kanoute returned from injury to hit the winner as Sevilla beat Recreativo Huelva 1-0 in a hard-fought Andalusian derby.
Kanoute has been out for several weeks with a muscle strain but returned to action last night and marked it by bagging the only goal of the game after 63 minutes.
Elsewhere Real Betis defeated Numancia 4-2, Deportivo edged past Espanyol 1-0, Osasuna and Athletico Madrid finished goalless, Mallorca and Athletic Bilbao drew 3-3 and Racing Santander beat Sporting Gijon 1-0.
AZ ALKMAAR and Ajax continue to set the standard in the Eredivisie with both teams claiming convincing victories yesterday.
AZ returned to the top of the table with a 3-0 rout of FC Twente. Brazilian striker Ari opened the scoring after 36 minutes with Mounir El Hamdaoui quickly adding another.
Ari then notched his second goal to stretch AZ’s unbeaten league run to eight matches.
They are joined on 22 points by Ajax, who enjoyed a 5-2 hammering of Sparta Rotterdam.
Goals from Klaas Jan Huntelaar, Luis Suarez, Evander Sno, Kennedy Bakircioglu and Leonardo earned the Amsterdam club their fifth successive league triumph.
Sparta managed to get on the scoresheet through Joshua John and Yuri Rose, but that was as good as it got for the visitors who suffered their third defeat in four matches.
LYON preserved their four-point lead at the top of Ligue 1 with a 1-0 win at Monaco thanks to a goal by striker Fred on Saturday. The seven-times French champions reshuffled their team after a 2-0 Champions League win over Steaua Bucharest and the changes paid dividends when usual second- choice players Fred and Kim Kallstrom combined to secure the points.
Lyon lead the standings with 30 points from 13 games ahead of Marseille, who kept up the pressure in second place with a 3-0 win at promoted Grenoble.
Bordeaux are third on 24 points after a 2-0 win at home to Auxerre while St Etienne slumped to a fifth successive Ligue 1 defeat to remain in the bottom three after being beaten 3-0 at home by Stade Rennes while PSG beat Lille 1-0 thanks to a Ludovic Giuly goal.
Meanwhile, Saint Etienne last night appointed former Tottenham sporting director Damien Comolli to a similar role with Les Verts.
BAYERN MUNICH closed to within a point of new leaders Bayer Leverkusen when Luca Toni and Franck Ribery combined to give them a 2-1 win at Schalke 04 yesterday.
Toni, back after a rib injury, supplied a cool finish to give Bayern an early lead.
Schalke were level almost immediately through Jefferson Farfan but Ribery scored his fourth goal in four league games to put Bayern back in front with half an hour gone and the champions held on for a fifth successive league win.
Hoffenheim’s own five-match winning run came to an end when Hertha clinched a surprise victory with a goal from Andriy Voronin midway through the second half.
Hoffenheim’s defeat saw Bayer Leverkusen climb above them on goal difference, with 25 points from 12 games, after their 3-3 draw away to Karlsruhe on Saturday. Hoffenheim are second, with Bayern third on 24 points.
JOSE MOURINHO’S Inter grabbed an injury-time goal to see off Udinese 1-0 at the Giuseppe Meazza yesterday.
Substitute Julio Cruz struck with just seconds remaining to send the Nerazzurri back to the top of Serie A.
Milan missed the chance to go top after being pegged back at the death against Lecce. Ronaldinho opened the scoring after 80 minutes but Andrea Esposito grabbed the equaliser for Lecce in injury time. Elsewhere, evergreen Juve forward Alessandro Del Piero marked his 34th birthday with a goal to help Juve to a 2-0 victory over Chievo. Vincenzo Iaquinta added the second on the rebound from a saved penalty after Andrea Mantovani had handled. Napoli continue to hover near the top after claiming a 2-0 win at home to Sampdoria Fiorentina edged past Atalanta 2-1, Genoa hammered Reggina 4-0, Lazio were 3-0 winners at home to Siena while Catania beat Cagliari 2-1.