The Australian has endured a miserable 2014, winning just three times on Tour since January's run to the Apia International in Sydney.
Tomic's rotten run has seen him, once ranked as high as 27 two years ago, drop out of the world's top 100, placing his chances of making next month's US Open in severe doubt.
He has also seen teenage sensation Nick Kyrgios capture the hearts of Australian fans after a mesmerising run to the Wimbledon quarter-finals, accounting for Rafael Nadal en route to the last-eight.
However, Tomic put all that aside with a strong showing on the Bogota hard courts, opening the ATP 250 tournament with a comfortable victory over a man now ranked just 16 places below him.
The 21-year-old, given a wildcard for the Colombia event, fired 10 aces down and took 86 per cent of points on first serve, showing too much class for Dustov.
Tomic will face either Japan's Tatsuma Ito or home hope Alejandro Falla in the second round.
In other main-draw action on Monday, America's Alex Kuznetsov overcame Adrian Mannarino 6-4 7-6 (7-3).
A tight contest featured only one break of serve, handing Kuznetsov the first set, while the Frenchman was only able to take three points off the American's serve in a second set decided after a tie-break.
Argentine Guido Pella also advanced, thrashing local hope Eduardo Struvay 6-3 6-4 in an hour and three minutes.