Fourth seed Clijsters comfortably defeated another former world number one, Dinara Safina of Russia, 7-5, 6-2 in a match that was delayed by almost two hours by heavy showers.
But it was the early exit of third seed Dementieva that was the major surprise of the second round.
"I was not feeling well and I think I was affected by the weather," she told reporters after her loss. "I think that was probably the worst match of mine for a long, long time.
"I was just not into the game. I couldn't really focus, my concentration was not there and I was just not feeling well," she added, citing the humid conditions in the days before Wednesday's rain.
Pavlyuchenkova will meet 13th seed Shahar Peer of Israel, who defeated Spanish qualifier Nuria Llagostera Vives 6-3, 6-2.
"I had nothing to lose against Elena and I just wanted to enjoy things and put on a good performance," said the 19-year-old, who won her second WTA event in Istanbul last week.
Three-times Grand Slam winner Sharapova looked in impressive form as she crushed Germany's Andrea Petkovic 6-3, 6-1.
Wimbledon runner-up and 2006 Cincinnati champion Vera Zvonareva survived multiple rain delays and a 5-2 deficit but fought back to win the third set and defeat fellow Russian Maria Kirilenko 7-5, 2-6, 7-6 (2).
Zvonareva will face Flavia Pennetta, who defeated Romanian qualifier Monica Niculescu 6-0, 6-1 earlier in the day.
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