Singh beat Alex Cejka 8 and 7, while Campbell defeated Fredrik Jacobson 6 and 5.
"If I play like I'm doing right now for the next two or three years, I'm going to contend for the world No. 1 spot. That's my goal," Singh said.
Thomas Bjorn and Tim Clark also won 36-hole matches, although both had to overcome deficits. Clark got past Stephen Leaney 3 and 2, and Bjorn beat Len Mattiace 4 and 3.
The four seeded players had byes in the first round and play today in the quarterfinals: defending champion Ernie Els, going for a record-tying fifth title, vs. Clark; PGA champion Shaun Micheel vs. Singh; British Open champion Ben Curtis vs. Campbell; and Masters champion Mike Weir vs. Bjorn.
The tournament invites players based on a ranking system that takes into account performances in the four majors. The defending champion and No. 1-ranked player qualify automatically.
Top-ranked Tiger Woods, though, passed up the event, as did Phil Mickelson, Jim Furyk, Davis Love, David Toms and Kenny Perry.
- JACOBSEN LEADS: Peter Jacobsen birdied his first six holes -- and 11 overall -- while shooting a 9-under 63 to set a first-round tournament record and take the lead at the Chrysler Classic of Greensboro on Thursday in Greensboro, N.C.