Poulter had four birdies en route to a 3-and-2 victory over John Senden. Poulter, who defeated Luke Donald in last year's match play final, never trailed Thursday.
He had a birdie at the third hole and was 3-up after 12. Senden posted his lone hole win at the 14th, but Poulter won No. 15 and halved 16 to lock up the win.
Charl Schwartzel used an 18th-hole birdie to halve his match with Nicolas Colsaerts in the day's only match without a winner.
Graeme McDowell won two of the last three holes in a 1-up win over Robert Karlsson while Sergio Garcia had birdies over three of his last five for a 2-and-1 win over Alvaro Quiros. Paul Lawrie had a similar finish in his 2-and-1 victory over Peter Hanson.
Rafael Cabrera-Bello built an early lead in getting past Martin Kaymer 3-and-2.
The tournament is contested in group play Thursday and Friday with the top two in each three-man group advancing to Saturday's quarterfinals. The semifinals and finals are scheduled for Sunday. Each of the 24 golfers is to play two round-robin matches Friday.
Joining Cabrera-Bello and Kaymer in their group is Robert Finch. Tom Lewis is in the same group with Poulter and Senden while Branden Grace completes the Bjorn-Snedeker group. Darren Clarke will play Rock and Rose in their group Friday.
Jbe Kruger was placed in the group with McDowell and Karlsson and Tetsuji Hiratsuka goes against Garcia and Quiros. Camilo Villega is in the group that includes Hanson and Lawrie and Retief Goosen completes the Schwartzel-Colsaerts group.