The win marks the 2018 Miami Open runner-up's first triumph at the event since that run to the final.
No.6 seed Ruud eased past Henri Laaksonen 6-1 6-2, while No.9 seed Sinner defeated Emil Ruusuvuori 6-4 3-6 7-6 (10-8) in two hours and 40 minutes.
Several seeds were beaten included No.13 seed Diego Schwartzman who went down 4-6 7-6 (7-3) 6-4 to Australia's Thanasi Kokkinakis not long after fellow Australian Nick Kyrgios had upset No.5 seed Andrey Rublev in less than an hour.
Seeds Lorenzo Sonego, Grigor Dimitrov, Reilly Opelka and John Isner also exited.
Gael Monfils defeated Oscar Otte 7-6 (11-9) 6-1, Pablo Carreno Busta won 6-3 6-2 over David Goffin and 10th seed Cameron Norrie won 7-6 (7-5) 6-4 over Jack Draper.