The world number one, bidding for her 23rd grand slam, eased to a 6-3 6-3 victory over fellow American King at Arthur Ashe Stadium on Thursday.
Williams dropped just one game in her only previous meeting with King – at Flushing Meadows in 2014 – and while that changed, the result was never in doubt.
The 34-year-old hit 19 winners in the first set as she dominated with her power, before cruising through the second.
The match was complete in just 64 minutes, with Swede Johanna Larsson awaiting Williams in the third round.
