After disposing of the French fourth seed, Belgium's US Open champion now faces Anna-Lena Groenefeld.
However, in the end, the 2010 British Open champion was no match for Watson.
It was a disappointing day for US Open champion McDowell and ex-Ryder Cup captain Colin Montgomerie.
"It's disappointing because I started off so poorly again, " said the three-time US Open champion.
This year's entry list includes new No. 1 and Australian Open champion Victoria Azarenka.
The Australian Open champion was joined in the third round by 2003 Toronto champion Andy Roddick.
"I haven't played that well in a long time, " said the 2009 French Open champion.
"I wasn't happy with the way I played, " said Scholten, last year's UK Open champion.
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The 2011 U.S. Open champion bemoaned her own mental state at crucial points in the match.
Current Open champion Ernie Els is among those one further back following a disappointing 72.
Serbia's 2008 French Open champion will next play Dutch world No. 91 Michaella Krajicek.
In the women's section, 16-year-old Ashleigh Barty stunned former French Open champion Francesca Schiavone 6-0 6-3.
Williams, the reigning Wimbledon, Olympic and U.S.Open champion, saw off 19-year-old Sloane Stevens 6-4 6-3.
Sharapova, the reigning French Open champion, lost to Serena Williams in straight sets in the Spanish capital.
Victory over Kelly would bring Casey a quarter-final against Retief Goosen or US Open champion Angel Cabrera.
Hunter will take on David Gray, the reigning Scottish Open champion, who beat Stockport's Nick Dyson 5-2.
Sam Stosur rounded off Tuesday's play with a 6-4 6-4 win over French Open champion Francesca Schiavone.
Argentine Agustin Calleri (16) earlier defeated last year's finalist and French Open champion Albert Costa 6-4 6-2.
Williams won the Madrid title last week and next faces French Open champion Li Na of China.
The 2009 Open champion Stewart Cink and Matt Kuchar will form the opposition for McIlroy and McDowell.
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Harrington, the Open champion, took the week off but still held on to the final qualifying spot.
Garcia once led Maria Sharapova, the reigning French Open champion, by a set and break at the tournament.
"I really want to see those guys play in the final, " said two-time French Open champion Jim Courier.
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Australian Open champion Azarenka had been looking for her fifth title this year, but was steamrollered by Williams.
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In July the club will open an 18-hole golf course, designed by former British Open champion Tom Weiskopf.
The US Open champion leads the four-man event - for the season's Major winners - by five strokes.
Now that Maria Sharapova, the French Open champion, is No. 1 again, it seems the field is narrowing.
Govortsova put out former French Open champion Francesca Schiavone in her opening match at the clay court event.
After Sharapova and Kvitova, the highest-ranked player remaining in the last eight is U.S. Open champion Sam Stosur.
McIlroy's European Ryder Cup teammate Justin Rose leads the way on five-under-par alongside Irish Open champion Jamie Donaldson.
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