The Colombian became the first player from his country to break into the top 100 of the ATP Rankings since Mauricio Hadad in 1996. In 2006, Alejandro qualified a career-high five times into the main draw of ATP tournaments. In his second tournament of the year, he reached the final of the Mexico City Challenger. He then went on to earn points for his country in a Davis Cup tie against Paraguay Davis Team. Then later in April, he won the Bogotá Challenger. At Roland Garros, he reached the second round after defeating Justin Gimelstob, though he lost to Roger Federer in the second round. A few weeks later at Wimbledon, he managed to beat Nikolay Davydenko in a four-set thriller. His victory over Davydenko was his first win over a top-10 player, and a first ever for a Colombian player. However, he was then defeated in the second round by Philipp Kohlschreiber in another four-set match. He then reached the second round in the US Open. In the first round, he beat Juan Martín del Potro in four sets, before being defeated by Dmitry Tursunov in straight sets.
Falla almost caused a sensation in the first round of Wimbledon in 2010, winning the first two sets against defending champion Roger Federer and serving for the match at 5–4 in the fourth set (he was three points away from winning), before Federer eventually won 5–7, 4–6, 6–4, 7–6, 6–0.
His best result in a Grand Slam was in 2011 at the French Open. Falla reached the fourth round, where he lost to the unseeded Juan Ignacio Chela.
In the 2014 Gerry Weber Open in Halle, Falla rallied to beat 2011 champion Philipp Kohlschreiber 5-7, 7-6 (5), 6-4 to become the first Colombian to reach the final of a grass-court tournament. He lost to six-time champion Roger Federer in the final.