Gasquet, the favourite to claim the ATP 250 title played on hard courts in Bogota, slumped to a 6-3 6-4 loss to the Dominican Republic's Victor Estrella Burgos.
Frenchman Gasquet never got going and had his serve broken three times, beaten in just an hour and five minutes by the world number 92.
Gasquet served at just 48 per cent against Estrella Burgos, who is 33 and the eighth seed at the event.
It opened up the draw for Australian wildcard Tomic, who overcame Canadian third seed Vasek Pospisil 6-4 6-4.
Tomic, likely to be back in the top 100 on Monday, broke once in each set to reach his first ATP World Tour semi-final since Sydney in January.
On the other side of the draw, defending champion Ivo Karlovic faces fellow veteran Radek Stepanek.
Big-serving Croatian Karlovic continued his fine form, sending down 21 aces in a 6-3 7-6 (8-6) win over the Chinese Taipei's Jimmy Wang.
For Karlovic, the second seed who was runner-up on the grass at Newport on Sunday, it was his 250th win on the ATP Tour.
Karlovic faces fourth seed Stepanek next after the Czech beat Colombian sixth seed Alejandro Gonzalez 6-4 6-4.