Bengoechea was in the 1977 second round of the Wimbledon junior tournament . The following year he became a professional tennis player and was able to win his first and only individual title on the ATP Challenger Tour in 1980 . Ten years later he won the only double title of his career with Christian Miniussi , also at a Challenger tournament. In the course of his career, he never won a title on the ATP World Tour . In addition, he only managed a positive season record in 1987 with 26:17 wins. In that year he also reached his highest ranking in the tennis world rankings ; after participating in the semi-finals in Hamburg , Florence , Gstaad , Hilversum and Barcelona , he was ranked 21st in the individual. He held the best placement in doubles in 1985 with position 153. He played his last continuous professional season in 1991; In 1994 he failed in his only tournament in the qualification and in 1995 he entered the double competition of a lower-class satellite tournament with a wildcard from the organizer. In 2000 he played two tournaments on the ATP Seniors Tour and became the Argentine over 40s champion, as a result, he was led to position 11 in the senior ranking list. After a first round defeat in 2002, however, he no longer appeared on the Senior Tour.
His best individual result in a Grand Slam tournament was reaching the third round at the French Open , which he achieved twice. In 1981 he was there in the doubles competition also in the third round. In mixed he reached the second round of the French Open in 1985.
In 1986 Bengoechea played two doubles games for the Argentine Davis Cup team . He was able to win both games, but was subsequently no longer considered. In 1996 he was team principal of the Argentine Davis Cup team.