Mario Kempes was born in Belville, Cordoba, to an ex-amateur footballer (also called Mario), who enthused in his son a love of the game. Kempes began his career at his local club Instituto Cordoba and was soon noticed as a great talent. By the time of the 1974 World Cup in West Germany, and at only 20 years old, Kempes was already established as a first team regular for Argentina. However, they played badly, losing to Poland, drawing with Italy and managing their only win of the campaign against lowly Haiti (who scored a goal past the Argentines, despite being beaten 7-0 by Poland). In the second round, they fared even worse, receiving a 4-0 thrashing from Cruyff's Dutch team, as well as a defeat to Brazil and a 1-1 draw with East Germany, to finish bottom of the group. Kempes had failed to score a sigle goal.

After the World Cup, Kempes moved to Rosario Central, where he scored 85 goals in 105 matches in the two seaons he was there. He was establishing himself as a ferociously efficient goalscorer - flamboyant but hard-working, and especially dangerous just outside the penalty area where he was remarkably fast and had a lethal long range shot. In 1976, Kempes moved to Spanish team Valencia, where he continued his awesome record with 24 and 28 league goals in his first two seasons (top goalscorer in La Liga on both occasions), and was adored by fans.

In the 1978 World Cup, Argentina were hosts and Kempes returned home as the only foreign-based player selected. He was determined to show that he could reproduce his club form on the greatest stage of all. However, it started slowly in the group stage and a defeat to Italy meant that Argentina were runners-up and would have to change venue - from Buenos Aires to Rosario. Kempes, who had failed to score in the first round, was back at his old home stadium and it seemed to spur him on to show his full potential. First, Kempes helped defeat Poland by scoring both goals in a 2-0 victory. A 0-0 draw with Brazil was followed by a 6-0 thrashing of Peru, in which Kempes scored a further 2 goals. Kempes, and squad in general, returned to Buenos Aries for the final as a very different prospect from the team in the first round. Kempes dominated the final against the Netherlands, scoring two and setting up Bertoni for their third in a 3-1 victory. Kempes finished as top scorer.

Kempes continued winning trophies with Valencia, as "El Matador" helped the club to the Copa del Rey in 1979 and the European Cup Winners' Cup and European Supercup in the following year. In 1981, Kempes moved back to Argentina to play for giants River Plate, where he won the national league championship.

In 1982, the World Cup was in Spain. Kempes had lost his place as the squad's star to a youngster called Maradona. The tournament was disappointing for Argentina, with a loss to Belgium in the first round and defeats to Italy (2-1) and Brazil (3-1) in the second round group stage, where they were knocked out.

After the World Cup, Kempes stayed in Spain to rejoin Valencia for another couple of seasons. In all, Kempes made 247 appearances and scored 146 goals in all competitions for the club. He later moved to Spanish minnows Hercules, before a number of clubs in Austria and one in Chile. In 1996, he joined Indonesian league champions Pelita Jaya as a player-coach, playing his final game that year. Kempes then worked as a coach in Albania, Venezuela and in Bolivia, where he won his first title as a manager with The Strongest FC in 1999. Kempes now works as a pundit for ESPN in America.