All three were taken to three sets in California.

Raducanu beat in-from Carolina Garcia of France 6-1, 3-6, 6-1, with the Briton converting six of her eight break points in a clinical performance.

Romania's Halep faced neutral player Ekaterina Alexandrova and also broke six times, aided by 14 double faults from Alexandrova.

The 2015 champion won 6-2, 4-6, 6-2 and will play 17-year-old American Coco Gauff next.

Gauff beat compatriot Claire Liu in straight sets.

Świątek had to come from behind to defeat Ukraine's Anhelina Kalinina in a match lasting two hours.

Superior serving proved to be the difference, as Świątek produced five aces to Kalinina's one and only three double faults, versus nine for Kalinina.

The Pole also won 68 per cent of points on her first serve - more than 20 per cent higher than Kalinina's record.

Świątek won 5-7, 6-0, 6-1.

Spain's Garbiñe Muguruza and Czech Karolína Plíšková became the first top-10 seeds to be knocked out, losing to American Alison Riske and Montenegro's Danka Kovinić, respectively.

Ukraine's Elina Svitolina also came unstuck, losing to Harriet Dart of Briton despite taking the first set.

The men's tournament is still in the first round, with Australian Jordan Thompson eliminating Belgium's David Goffin among the notable results.

Americans Tommy Paul and Steve Johnson, veteran Argentine Facundo Bagnis, Dutchamn Botic van de Zandschulp and Poland's Kamil Majchrzak also secured passage to round two.

Paul will face Olympic champion Alexander Zverev of Germany in the next round.