Tabilo is the first Chilean to beat a world number one since Fernando Gonzalez beat Roger Federer at the ATP Finals in 2007.
He will play Karen Khachanov in the next round after the Russian 16th seed beat Argentina’s Francisco Cerundolo 6-2 6-4
It means six-time champion Djokovic will fail to reach at least the quarter-finals in Rome for the first time since 2006.
The 36-year-old, who is yet to reach a final in 2024, has played just six matches on clay this year as he prepares for the defence of his French Open title.
The tournament at Roland Garros begins on 26 May.
Elsewhere, Aryna Sabalenka eased through to the last 16 in Rome with a comfortable straight-set win over Dayana Yastremska.
The Belarusian Australian Open champion did not drop a single service game as she beat Ukrainian Yastremska 6-4 6-2 in one hour 28 minutes.
She will play Ukraine’s two-time winner Elina Svitolina or Russia’s Anna Kalinskaya in the next round.
