Nicknamed "El Turco," Cabalén first came to motorsport via motorcycles, purchasing an HRD machine in 1948. Within a fortnight he had won a race in Bell Ville. After four further events, a crash at Calvez left him with fractures to both his tibia and fibula that required six months to heal. On medical advice he abandoned motorcycles and worked for a period at his brothers' lorry company before making the switch to four-wheeled competition.
Cabalén made his Turismo Carretera debut on July 1, 1950, and went on to contest the Carrera Panamericana twice. In 1953, co-driven by Guillermo Ibanda, he finished 36th overall and third in the Turismo Especial class in a race overshadowed by the deaths of several competitors, including Felice Bonetto. The following year, paired with Mexican co-driver Genaro Silva, he finished 33rd and seventh in class.
Following the example of his mentor and friend Juan Manuel Fangio, Cabalén travelled to Europe. At the 1955 Mille Miglia, co-driven by Italian Ottavio Guarducci, he finished fifth in the Alfa Romeo Giulietta Sprint Veloce category. He also competed in the 10 Hours of Messina, sharing a Ferrari 500 Mondial with Venezuelan Joao Rezende dos Santos. The pair finished second behind Maurice Trintignant and Eugenio Castellotti and won their class.
At the 1960 Argentine Grand Prix, Cabalén served as reserve driver for fellow Argentine Nasif Estéfano, who was entered in a Maserati 250F. Cabalén drove only during the final qualifying session, posting a time two-tenths of a second slower than Estéfano but ahead of Ettore Chimeri and Antonio Creus in their own 250Fs.
Back in Argentina from 1961, Cabalén re-committed to Turismo Carretera with a Ford V8, claiming his first victory at Villa Carlos Paz and finishing runner-up in the championship that year behind Oscar Alfredo Gálvez. In 1966 he won the Gran Premio de Turismo driving a Ford Mustang, and in 1967 he was a member of Team Racing Ford Argentina.
Cabalén died on August 25, 1967, during a test session at the temporary SOMISA de San Nicolás circuit, where he was preparing for the 6th Gran Premio de TC General Manuel Savio. On one of his runs his car left the road at more than 205 km/h, rolled multiple times, and caught fire, coming to rest approximately 100 metres down the circuit. Team mechanic Guillermo Luis "Pachacho" Arnáiz was in the car alongside him; both men were killed when the fibreglass bodywork and high-octane fuel burned rapidly, trapping the occupants. Cabalén is buried in the Cementerio de San Jerónimo in Córdoba Province. The Autódromo Oscar Cabalén, the permanent racing circuit serving Córdoba, was subsequently named in his memory.