Woods has won seven straight PGA Tour events, four short of the all-time record held by the late Byron Nelson.
Although golf's leading star advanced to the next round, the tournament will proceed without players ranked second through eighth in the world. Jim Furyk (No. 2), Phil Mickelson (4), Retief Goosen (6), Vijay Singh (7) and Luke Donald (8) were all defeated Thursday.
Furyk was beaten by Chad Campbell in 19 holes, Mickelson was a 3&1 victim of Justin Rose, and Goosen suffered a 1-up setback against Niclas Fasth. Singh went down in 19 holes to Stephen Ames and Donald fell to Aaron Baddeley on the 18th hole.
Charles Howell III, this year's leading money winner, moved into the third round and will next play Rose.