Burillo 1991 professional tennis player, reaching the ATP Challenger tournament in Sao Paulo, the doubles final. The following year, he beat Boris Becker in the second round of the ATP Tournament Barcelona and won as a qualifier in 1993 his only individual title at the tournament in Bologna. He also reached the final of Florence, where he lost to Thomas Muster. In 1995 he won by a final victory over Carlos Moyá the Challenger tournament in Barcelona, he also stand in the final of Palermo, which he lost narrowly to Francisco Clavet. After he was sidelined in 1996 due to an ankle surgery, he won the following year, on the side of Alberto Berasategui his only doubles title on the ATP World Tour. Its highest listing in the tennis world ranking he reached in 1995 with position 43 in singles and in 1996 with position 100 in doubles.
His best individual result at Grand Slam tournaments was reaching the third round of Wimbledon 1994. In doubles he stood in 1998 in the second round of the French Open.
Burillo 1994 played two single matches for the Spanish Davis Cup team. In the quarter-final match against Germany, he lost his first singles match against Michael Stich in four sets. His second singles match against Marc -Kevin Goellner he could not win in two sets, but it was meaningless, since Spain already lagged uncatchable.
After the end of his professional career Burillo was coach of Julián Alonso.