Dimitrov, a two-time major semifinalist, bowed out 7-6 (4), 6-2, 6-4 in the third round against Fernando Verdasco, who is ranked 35th and seeded 30th.
Sharapova was staring down the barrel of falling at first hurdle in a Grand Slam tournament for the first time since the 2010 Australian Open when trailing 3-0 in the third, but the former world number one dug deep and reeled off six straight games to edge into round two.
Halep said in her post-match interview that she struggled initially against the left-hander's shots with topspin.
From there, Halep's serve and shots that pulled Townsend around the Court Philippe-Chatrier finished the job.
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Her next opponent, Andrea Petkovic of Germany, beat Bethanie Mattek-Sands 6-0, 7-6 (5) to reach the third round.
Third seed and 2016 champion Garbine Muguruza defeated 2009 victor Svetlana Kuznetsova 7-6 (7/0), 6-2. She won 12 consecutive points on her serve in one stretch.
The 29th seeded Frenchman then won three straight games to trail 3-5 but could not stop Nadal from serving out the opening set to win it 6-3.
The most-anticipated matchup for a quarter-final spot at Roland Garros pits 23-time major champion Williams against five-time major champion Sharapova, who has won two of her five majors at Roland Garros.
Pliskova reached the third round with a 3-6, 6-4, 6-1 victory over 2015 French Open runner-up Lucie Safarova.
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The top-seeded Romanian has never lost to Petkovic, and four of her seven wins have been on clay.
There was another upset as unseeded Ukrainian Lesia Tsurenko defeated 19th-seeded Slovak Magdalena Rybarikova 6-2, 6-4.
In other men's singles results, Italian Fabio Fognini battled past 16th-seeded British number one Kyle Edmund 6-3, 4-6, 3-6, 6-4, 6-4 in a match lasting three and a half hours.
Duckworth, who missed the French Open a year ago because of foot surgery, has never won a match at the clay-court event in four appearances. Their match was suspended for rain late Friday.
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