Falla endured the long match, which was delayed Wednesday due to rain and resumed Thursday morning, after his three-hour marathon against American John Isner in the first round, beating Mahut 6-4, 6-3, 4-6, 4-6, 7-5.
Falla, who is ranked 73rd by the Association of Tennis Professionals, became the first Colombian ever to reach the third round of Wimbledon, after falling in the second round last year.
“Very happy to be in the third round of Wimbledon,” he tweeted following the match. “Thanks to everyone for the messages and for your support,” he added.
The Colombian will face Uzbek Denis Istomin in the next round at the All England Lawn Tennis and Croquet Club in England.