Lautaro Acosta had the best chance for the hosts early in the second-half but blazed over with only goalkeeper Gustavo Munua to beat.
Racing were reduced to 10 men when Papa Kouli Diop was dismissed for a second yellow card on 80 minutes. Levante nearly made the extra man count, but Tono Martinez saved Nabil El Zhar's late effort.
Levante were happy to sit deep and allow Racing to make most of the play, but the home side, who had been so impressive despite losing 4-3 to Valencia in week one, struggled to create any clear-cut chances.
Munua was not forced into action until the 31st minute when Racing debutant Christian Stuani, who had played at Levante last season, shot left-footed straight at the `keeper.
The visitors best effort of the match came minutes later when Jose Barkero's free-kick was well saved by Tono and Sergio Ballesteros fired the rebound over.
Pedro Munitis looked the most likely to create for Racing and his pass released Acosta whose shot from an angle was blocked by Munua.
Racing started the second period brightly and Acosta had their best chance of the game when after turning Ballesteros he blazed over from 10 yards.
The hosts were reduced to 10 men as many minutes remaining when Diop received a second yellow card for an unnecessary challenge on substitute Ruben Suarez.
Levante had not shown any attacking intent in the second half but pushed on with the numerical advantage.
Suarez smashed a free-kick in a dangerous position into the wall before El Zhar's fierce left-foot shot was well held by Tono.
