Rublev, seeded six, lost 7–6 (7/5), 4–6, 6–3 to German qualifier Yannick Hanfmann, ranked 101st in the world.
Eighth seed Italy’s Sinner was defeated by Argentina’s Francisco Cerandolo 6-7 (3/7), 6-2, 6-2.
In the women’s draw, Inga Swiatek extended her winning streak to 14 matches with a 6-3, 6-4 success over Donna Vekic.
World number one Swiatek will take on Elena Rybakina in the quarter-finals after going through her toughest match of the tournament so far.
Its bid for a third title in as many years has dropped from the two to six seeds.
