Ranked 275th, the 20-year-old Donati showed off an aggressive game, often dictating play from within the baseline to the approval of a vocal crowd inside the Foro Italico’s main stadium.
Despite losing the first set to the Colombian, Donati showed great fighting spirit to bounce back and win the next two sets to set up a meeting with sixth-seeded Tomas Berdych.
Also, 15th-seeded Kevin Anderson of South Africa narrowly edged Florian Mayer of Germany 7-6 (7-3) 4-6 7-6 (7-4).
Elsewhere on the red clay, Leonardo Mayer of Argentina eliminated another Italian wild card, Federico Gaio, 6-3 6-4.
And Jeremy Chardy of France beat Lukas Rosol of the Czech Republic 7-6 (7-0) 6-4 and will next face third-seeded Andy Murray.