Naomi Osaka ensured she will remain world number one after cruising to a 6-4 6-3 win over Hsieh Su-wei in her opening match at the Stuttgart Open on Thursday.

The two-time grand slam champion reached the top of the rankings at the Australian Open but has since struggled for form, losing to Hsieh at the Miami Open in her last match before this week's WTA Premier tournament.

But with former number one Simona Halep ruled out with a hip injury, Osaka needed only to progress through the second round to secure her status, with Petra Kvitova unable climb to the summit.

Third-ranked Kvitova would still have needed to win the title in Germany to capitalise if Osaka had slipped up, but that scenario did not materialise.

The Japanese needed just a single break to take the opening set from Hsieh and broke on a couple of more occasions in the second to complete a routine win.

She will face Donna Vekic in the quarter-finals on Friday.