Burillo became a professional tennis player in 1991 and reached the doubles finals at the ATP Challenger tournament in São Paulo . The following year he defeated Boris Becker in the second round of the ATP tournament in Barcelona and won his only individual title at the tournament in Bologna as a qualifier in 1993 . He was also in the final in Florence, where he lost to Thomas Muster . In 1995 he won the Challenger tournament in Barcelona by beating Carlos Moyá in the final, and he was also in the final in Palermo , which he just lost to Francisco Clavet . After he had to pause in 1996 because of an operation on his ankle , he won his only double title on the ATP World Tour the following year alongside Alberto Berasategui . He reached his highest ranking in the tennis world rankings in 1995 with position 43 in singles and 1996 with position 100 in doubles.
His best individual result in Grand Slam tournaments was reaching the third round of Wimbledon in 1994. In doubles, he was in the 1998 round of 16 of the French Open .
Burillo played two individual games for the Spanish Davis Cup team in 1994 . In the quarter-finals against Germany he lost his first individual against Michael Stich in four sets. He was able to win his second individual against Marc-Kevin Goellner in two sets, but it was meaningless, since Spain was already unreachable.
After the end of his professional career, Burillo was the coach of Julián Alonso .