Evans, ranked 81st in the world, overcame top seed and Monte Carlo Masters finalist Dusan Lajovic of Serbia 7-5 6-3.
British number two Norrie saved two match points to beat Chile’s Nicolas Jarry 6-3 4-6 7-6 (8-6).
They join British number one Kyle Edmund – who plays Spain’s Fernando Verdasco in the first round – in Rome.
Evans’ victory over Lajovic was a career-best on clay, with Lajovic ranked 57 places above him.
The 28-year-old beat Dutch tenth seed Robin Haase 6-2 6-4 in the first round of qualifying, while 45th-ranked Norrie, 23, beat Germany’s Peter Gojowczyk 5-7 7-5 6-3.
World number one Novak Djokovic, defending champion Rafael Nadal and 20-time Grand Slam champion Roger Federer are all in the Rome draw.