Third-placed Sevilla lost further ground on Real after goals from Sergio Garcia and new signing Ricardo Oliveira gave Real Betis a 2-1 win at the Sanchez Pizjuan and condemned their city rivals to a third consecutive league defeat.
Champions Real have 47 points from 22 matches behind Barca who host Sporting Gijon on Sunday. Sevilla are third on 38 while Betis move up to 13th with 25, easing the pressure on under-fire coach Paco Chaparro, and Racing stay 10th with 28.
Argentine forward Higuain grabbed the only goal at the Bernabeu when he raced on to Raul's headed pass, turned inside a sliding challenge from Cesar Navas and clipped the ball over Racing goalkeeper Tono into the far corner.
The lively Jonathan Pereira had a chance to level with 15 minutes left but Real keeper Iker Casillas raced out to block the forward's shot and Fabio Cannavaro cleared.
Raul equalled Alfredo di Stefano's club scoring record of 307 goals last weekend and almost grabbed the honour for himself in the first half with a near-post shot blocked by Tono.
"The team put in a big effort tonight," Higuain told reporters. "I am always happy to score and if I do it at home even better."
CLEAN SHEETS
Real coach Juande Ramos gave new signing Julien Faubert his first action since he joined from West Ham United last month. The French midfielder replaced in-form Dutch winger Arjen Robben with half an hour left but had few chances to make an impact.
Ramos said his side's failure to find a second goal had made the players nervous but added he was pleased with another clean sheet -- their sixth in seven games.
"We managed to grab another win and that gives the team confidence," he told reporters. "We are not conceding goals and got another three points and that's the important thing."
Sevilla had most of the best chances in a game littered with fouls but their night was ruined when midfielder Aldo Duscher was dismissed for a second yellow card with about 20 minutes left and Garcia scored immediately after.
Defender Melli fired a speculative ball forward and Garcia found space between the defenders to volley into the ground and over stranded Sevilla keeper Andres Palop.
Oliveira scored a second late on when he fired the ball under Palop. The Brazilian striker, Betis's top scorer with 22 goals in the 2004/05 season, was playing his first match since his return to the club from second-division Real Zaragoza.
Mali striker Frederic Kanoute snatched a consolation goal for Sevilla in added time with a precise header.
