But she will face 14th-seeded Russian Maria Kirilenko next after defeating Morita 6-1, 6-3 win in 66 minutes.
With sister Venus out of the tournament after being crushed in straight sets by Maria Sharapova on Friday, Williams was in no mood to be on court longer than necessary.
She had only dropped two games during the tournament ahead of this match and on a cool and breezy day easily won the first game for a 1-0 lead.
Japanese number one Morita held serve then pushed the American veteran hard on her service game, but Williams held and then stepped it up with a blistering backhand down the line, giving her a break for 3-1.
There was no stopping her, with Williams firing down the fastest women's serve of the tournament so far at 207 kilometres per hour (128 mph) on her way to taking the set in 31 minutes.
But the 15-time major-winner, who has an eye on the first calendar-year Grand Slam since 1988, wavered on her serve in the second set and Morita raced to 3-0 lead.
It was a short-lived advantage with Morita imploding and Williams reeling off six games in a row to easily clinch the match.