The Serbian appeared to be easing to victory when he took the first set, but his first-serve percentage dropped to 38 per cent in the second set and Falla took full advantage.
Falla struggled with his own delivery in the third but it did not prove fatal as he claimed a notable scalp.
In the last four he will face Canada's Vasek Pospisil, who rallied to beat Matteo Viola 3-6 6-3 6-2 and set up his first ATP Tour semi-final.
Second seed Kevin Anderson found life far easier than Tipsarevic as he dispatched Colombia's Santiago Giraldo in straight sets.
The South African broke three times on his way to a 6-3 6-3 win in 65 minutes and will next face Ivo Karlovic.
The Croatian's trademark serve was in good shape as he produced 22 aces in a 7-6 (7/5) 7-6 (7/3) win over Adrian Mannarino of France, the fifth seed.