FORT WORTH, 23 May 2015 (AFP) - The Englishman fired a two-under par 68 in the third round to stand on 10-under after 54 holes, hot on the heels of US standout Na, who fired a 69.
Poulter missed a seven-foot birdie putt at the 18th hole that would have pulled him level with Na entering Sunday's last round at Colonial.
Poulter, who has never won a stroke-play event on the United States, was voted along with Rickie Fowler the most "overrated" players on the PGA Tour in an anonymous poll of players conducted by Sports Illustrated last month.
Fowler answered with a victory two weeks ago at the Players Championship and Poulter, who has 1.89 million Twitter followers, could respond this week after already taking heat for playing in Texas rather than at Wentworth in a European Tour event in his homeland.
"Do you think I pay a lot of attention to what people think? 1.89 million people? I mean, seriously. Come on," Poulter said. "It's water off a duck's back. It has actually become quite funny, to be honest, so I take it a little bit tongue-in-cheek."
Critics saw Poulter as cheeky for skipping Wentworth but a new event this year, the British Masters in October, will count as his home event for 2015. But Poulter has played well at Colonial and not so well at Wentworth over the years.
"It's a golf course which hasn't been too kind to me over the years," he said. "My performances haven't been very good there."
Start times Saturday were advanced to the morning to avoid the worst of afternoon storms, but rain still pelted players much of the round.
Poulter opened with a birdie after dropping his approach three feet from the cup at the par-5 first, then added another birdie at seven with a 30-foot putt.
The Englishman's magical putter touch vanished as the back nine began, as he took three putts to get down from 3 1/2 feet for a double bogey at the 10th.
But Poulter answered with a six-foot birdie putt at 11 and holed a 32-foot birdie putt at 15 to grab a share of the lead at 10-under when playing partner Na made bogey, missed a five-foot par putt.
Na answered with a 14-foot birdie putt at 17 to reclaim the lead alone at 11-under and Poulter missed his birdie chance at 18 to leave the American alone at the top.
After a birdie at three and a bogey at the fifth, Na sank a seven-foot birdie putt at 11 to put himself in front.
American Charley Hoffman was third at 201 with countrymen Brandt Snedeker and Chris Kirk at 202 and compatriots Kevin Kisner, Brian Harman and George McNeill joined by South African Rory Sabbatini on 203.
A pack on 204 included Australian Adam Scott, Fiji's Vijay Singh, Canada's Adam Hadwin and Nick Taylor plus world number two Jordan Spieth, the reigning Masters champion.
Leading third-round scores on Saturday at the US PGA Tour Crowne Plaza Invitational at Colonial (USA unless noted, par-70):
199 - Kevin Na 64-66-69
200 - Ian Poulter (ENG) 65-67-68
201 - Charley Hoffman 66-69-66
202 - Chris Kirk 68-69-65, Brandt Snedeker 67-69-66
203 - Rory Sabbatini (RSA) 67-70-66, Kevin Kisner 67-69-67, Brian Harman 68-66-69, George McNeill 65-69-69
204 - Adam Scott (AUS) 72-66-66, Jordan Spieth 64-73-67, Jerry Kelly 67-70-67, Vijay Singh (FIJ) 69-66-69, Nick Taylor (CAN) 68-68-68, Adam Hadwin (CAN) 69-66-69, Boo Weekley 64-69-71
205 - Tony Finau 67-72-66, Colt Knost 66-73-66, Graeme DeLaet (CAN) 70-68-67, Ben Martin 66-71-68, Shawn Stefani 67-69-69, Marc Leishman (AUS) 66-69-70, Danny Lee (NZL) 66-69-70
206 - William McGirt 73-66-67, Zach Johnson 70-69-67, Fabian Gomeza (ARG) 70-69-67, Jason Bohn 69-69-68, Pat Perez 69-69-68, Kevin Streelman 71-69-66