Indian duo Jyoti Randhawa and Jeev Milkha Singh and Australia's Richard Green were also successful.
BBC: McDowell missed out on the US Masters earlier this year
China's Liang Wen-Chong, Thailand's Prayad Marksaeng and Indian Jeev Milkha Singh have been added to the field.
The other huge leaps into the top 50 came from Indian Jeev Milkha Singh and American Brett Wetterich.
Jeev Milkha Singh crashed to an 82 in the treacherous conditions and overnight joint leader Simon Dyson struggled to a 78.
Schwartzel is seeking his first win since claiming the 2011 Masters title and has a one-shot lead over India's Jeev Milka Singh.
The way that he played that second shot onto the green three feet from the hole after Jeev Milkha Singh's had shot left him five feet short -- wow!
First-round leader, Northern Ireland teenager Rory McIlroy, was a late starter but dropped back to seven-under alongside India's Jeev Milkha Singh after a bogey during his three holes possible.
And while Casey has reached the last two finals of the World Match Play in Arizona, Harrington has lost in the first round to Pat Perez and Jeev Milkha Singh.
India won their first track medal since Milkha Singh, father of golfer Jeev Milkha Singh, won the men's 400m in 1958 when Kavita Raut took bronze in the women's 10, 000m .
Welshman Woosnam, the 1991 champion, is off in the first group at 0800 (1300 BST), while Woods tees off alongside fellow American Stewart Cink and India's Jeev Milkha Singh at 1352 (1852 BST).
England's Danny Willett, Scot Paul Lawrie, Irishman Shane Lowry, Frenchman Julien Quesne, Indian Jeev Milkha Singh and Dane Thomas Bjorn are all in the group with current Open champion Ernie Els a shot further back.
Jim Furyk provided the last-day challenge to the leaders with a closing 67 for 16- under, with India's Jeev Milkha Singh fourth at 14-under and England's Oliver Wilson tied fifth with Colombia's Camilo Villegas after a brilliant closing 66.
Ahead of McIlroy and four shots back on the leaders in a tie for third are Jeev Milkha Singh of India and Colombia's Camilo Villegas, with Denmark's Soren Kjeldsen and Spain's Alvaro Quiros joining Americans Jim Furyk, Charley Hoffman and Kenny Perry on 11 under.
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