While American Jimmy Walker maintained his red-hot form this season with a commanding 5&4 win over South Africa's Branden Grace, matchplay expert and 2010 winner Poulter was upset 2&1 by American Rickie Fowler in the 64-player event at Dove Mountain.
Donald, who clinched the 2011 title, was hammered 5&4 by Italy's Matteo Manassero and world number six Johnson, the tournament's third seed who is known for his gritty play, was stunned 5&4 by South Africa's Richard Sterne.
Long-hitting Dustin Johnson, who has triumphed once and been a runner-up twice in just four starts on the 2013-14 US PGA Tour, also made an unexpected early exit, going down 4&3 to Swede Peter Hanson.
In total, there were nine upsets based on seedings from the 32 matches at Dove Mountain as the elite World Golf Championships (WGC) event once again lived up to its reputation for wild uncertainty and sharp swings in fortune.
Fowler took advantage of a sub-par performance by Poulter, who is renowned for his steely matchplay prowess, especially in the Ryder Cup.
"I knew it was going to be a tough match today, no matter if Poulter is not on his game," Fowler said. "He wasn't playing great, but I knew he was going to find a way to hang around.
"Obviously it feels good to get a win against him, against anyone. I'm excited for tomorrow."
Poulter, who succumbed to his third first-round exit in four years at Dove Mountain, wrote on Twitter: "Disappointed with my performance today do not deserve to move on. Congrats to @RickieFowlerPGA."
Fowler will next face his compatriot Walker, a debutant at Dove Mountain this week who is arguably the hottest player in the game after already securing three tournament wins on the US Tour this season.
"I played pretty solid all day, hit a lot of really good shots, made some birdie putts," said Walker, who sealed his victory over Grace with a 15-foot birdie putt at the par-four 14th.
"Branden had a couple of three-putts early in the round and that got me up to a pretty good little lead. Just kind of stayed nice and steady and then closed it off with two birdies there at the end."
The top two seeds advanced, Swedish world number three Henrik Stenson coming from one down after 13 holes to edge Thailand's Kiradech Aphibarnrat 2&1 and fifth-ranked Englishman Justin Rose battling past American Scott Piercy one up.
"I'm still in shock," said Stenson, the 2007 Match Play champion who is top seed this week with world number one Tiger Woods and second-ranked Australian Adam Scott opting not to play in the elite WGC event.
"It was a tough match. Kiradech is a good player. We both played well in the beginning. It was a bit back and forth there."
US Open champion Rose was also delighted to advance after trailing one down after 10 holes.
"I'm very happy to come through that match," said the Englishman, who has been recovering from tendinitis in his right shoulder.
"It wasn't a classic, but it doesn't need to be. It's all about doing enough on the day to get the match won."
Fourth-seeded Northern Irishman Rory McIlroy celebrated his first start on the US Tour this year with a 3&2 win over American Boo Weekley and former Masters champion Charl Schwartzel triumphed by the same margin over Kevin Stadler.
American Jordan Spieth, the 2013 US Tour rookie of the year, came from one down after seven holes to beat Spaniard Pablo Larrazabal two up while defending champion Matt Kuchar eased past Austria's Bernd Wiesberger 3&2.
American Bill Haas hammered Spaniard Miguel Angel Jimenez 4&3, Frenchman Victor Dubuisson crushed American Kevin Streelman 5&4 and veteran Dane Thomas Bjorn never trailed before beating Italy's Francesco Molinari 2&1.
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- Dove Mountain