At the Davis Cup, Sousa played two more dead rubbers, winning for the second time in three seasons over Cyprus' Christou and losing to Bosnian Damir Džumhur. Sousa reached several milestones in 2011. At the Challenger Tour, he won his first singles title at that level in Fürth in June. At the ATP World Tour, Sousa participated as a wildcard in the singles and doubles events in Estoril, losing in the second round of the former to Canadian Milos Raonic. He also made his first attempt at entering the main draw of a Grand Slam tournament, but fell in the qualifying rounds at the Australian Open, Wimbledon and the US Open. In October, Sousa's participation at the Sabadell Futures was his last presence in the main draw of a tournament in that category. He won three more singles and one doubles Futures titles, making his career titles at this level seven singles and nine doubles titles. Once again, Sousa was called for two dead rubbers at Davis Cup, winning over Martin Kližan from Slovakia and losing to Switzerland's Marco Chiudinelli. In October 2011, he hired Frederico Marques as a coach when he was ranked world number 220. At the 2012 Estoril Open, Sousa reached the quarterfinals of an ATP tour tournament for the first time, losing to Albert Ramos. At the 2012 French Open, he made his debut as a qualifier in the main draw of a Grand Slam tournament. He would lose in the first round to 20th seed Marcel Granollers in four sets. He did not progress past the qualifying rounds at the other three Grand Slam tournaments. He also entered main draw events at the Barcelona Open (lost to Frederico Gil in the 2nd round) and the Croatia Open (lost to Matthias Bachinger in the 1st round). At Challenger tournaments, Sousa won two singles titles out of three finals – Mersin and Tampere – and one doubles title at Fürth. His role at the 2012 Davis Cup rose in importance. Sousa played his first doubles rubber against Israel, partnering with Gastão Elias in a loss against Andy Ram and Jonathan Erlich. Ram also beat Sousa in a dead rubber – his last as of 2016. In September, Sousa played three rubbers against Slovakia. He won the first singles match over Lukáš Lacko but lost the doubles with Elias and his second singles match to Martin Kližan, meaning Portugal's relegation from Europe/Africa Zone Group I to Group II in 2013.