Poulter offset a lone bogey with four birdies at the par-70, 6,919-yard Phoenix Country Club for a 10-under 200.
Luke Donald was two strokes back after a 66 put him at 8 under. Gonzalo Fernandez-Castano and Daisuke Maruyama are a further two strokes back at 6-under.
Defending champion and overnight co-leader Padraig Harrington struggled Saturday and was tied for seventh after a 73.
Harrington beat Tiger Woods with a birdie on the second hole of a playoff last year. Woods, who won in 2004 and 2005, is not taking part this year.
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