Poulter, whose love of sleep means he happily describes himself as "half-man, half-mattress", was probably not best pleased to be out in the first match at 0725 local time at Dove Mountain.
And the Englishman's mood will not have been improved by a 2&1 defeat to American Rickie Fowler, who led from the fourth hole onwards and will now face compatriot Jimmy Walker in the second round.
Walker, who has already won three times in the 2014 PGA Tour season, secured the first victory of the day with a comfortable 5&4 win over South African Branden Grace.
After the opening three holes were halved, Fowler won three of the next four and needed only one birdie to do so, although 2010 champion Poulter then reduced his deficit with a birdie on the eighth.
A par on the 10th was enough for Fowler to move three up once again and although he gave the next hole back with a bogey six, a superb eagle on the par-five 13th - with Poulter in trouble over the green - restored a three-hole cushion.
In typical fashion Poulter refused to throw in the towel and won the 14th with a birdie from 18ft as Fowler missed from much closer, but further birdie chances went begging on the next three holes to seal his fate.
Finland's Mikko Ilonen had looked like creating a shock when he led Bubba Watson by two holes with six to play, but lost the next three holes and Watson - who claimed his first win since the 2012 Masters in the Northern Trust Open on Sunday - sealed a 2&1 win on the 17th.
"After number 11 I knew I had to fight hard and somehow I did it," Watson said.
"It's very tough, with all the media and attention around me after the win on Sunday, to focus enough on golf so hopefully this match scared me enough that I will focus a little harder."
There was better news elsewhere for two more of the 25-strong European contingent, with Peter Hanson three up on Dustin Johnson after 10 and France's Victor Dubuisson ahead of Kevin Streelman by the same margin at the turn.
Spain's Sergio Garcia had been two down after three holes against Australian Marc Leishman, but birdies at the sixth and 11th got Garcia back on level terms.
Poulter admitted he was beaten fair and square, writing on Twitter: "Disappointed with my performance today, did not deserve to move on, congrats to Rickie Fowler."
Fowler said on Sky Sports: "I knew it was going to be a tough match. He wasn't playing great today but I knew he was going to find a way to hang around and give me something at the end.
"Obviously it feels good to get a win against him and I am excited for tomorrow."
Sweden's Jonas Blixt was the next man into the last 32 with a 2&1 win over former US PGA champion Keegan Bradley and South African George Coetzee saw off Steve Stricker 3&1.
Stricker's participation in the event had been in serious doubt until his brother underwent a successful liver transplant at the weekend.
In the later matches, Rory McIlroy lost the first hole to a birdie from Boo Weekley but hit back with a two-putt birdie of his own on the par-five second to get back on level terms.