The Pole beat Akgul Amanmuradova 6-2, 6-4. Radwanska came to Kuala Lumpur on the back of winning in Dubai on Saturday, a victory which saw her reach a career high on the WTA rankings.
She was originally scheduled to play Amanmuradova on Tuesday, but the match was postponed when heavy rains and lightening played havoc with the schedule.
She finally took to the courts late Wednesday, but after winning the first set 6-2, play was called off when more rain fell with the score tied 3-3 in the second set.
In total, six hours of play was washed out on the third day of the tournament. Radwanska was fired up to finish off the match when play resumed on Thursday.
She will now meet Karolina Pliskova of the Czech Republic later Thursday. The victor of that game will play Taiwanese qualifier Su-Wei Hsieh.
Only two matches were completed on Wednesday. Besides Hsieh, fifth seed Petra Martic of Croatia also reached the quarter-finals.
The $220,000 BMW Malaysian Open at the Bukit Kiara Equestrian and Country Resort ends on Sunday.
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