Among the favourites for the title after the first-round defeats of the world's top two, Rory McIlroy and Tiger Woods, third seed Donald, the winner two years ago, was hammered 7&6 by the American Scott Piercy while Rose lost 4&2 to his Ryder Cup team-mate Nicolas Colsaerts.
Bubba Watson became the highest surviving seed at No.8, defeating Jim Furyk 1 up at the 22nd hole. The No.4 seed Louis Oosthuizen also lost out – 3&2 to Robert Garrigus.
Ireland's Shane Lowry, conqueror of McIlroy, beat Swede Carl Petterson 6&5.
At least one Englishman, Ian Poulter, Donald's predecessor as champion, managed to fly the flag as his compatriots floundered. He defeated Bo Van Pelt 3&1.
Colsaerts' victory over Rose was not that big a surprise. The Belgian won the Volvo World Match Play in Spain last year, had eight birdies and an eagle in his first-ever Ryder Cup game last September and began this week with a crushing 5&4 win over the American Bill Haas.
Rose won the first hole but could not match his big-hitting opponent's birdie on the long second and by the seventh was already three down. A birdie at the ninth and eagle on the 11th – both with 14-foot putts – hinted at a comeback, but Rose plugged his ball in a bunker on the next and Colsaerts hit his approach to two feet at the 14th. The 15th was halved with birdie threes – Colsaerts drove the green on the par four – and it ended on the following green when Rose three-putted.
After a 2&1 win over Scot Stephen Gallacher, Poulter fell behind to Van Pelt on the fourth, but a tee shot to three feet two holes later turned the tide. The American fluffed a chip at the next, Poulter birdied the eighth and further wins came at the start of the back nine.
Poulter held a 4-up lead after 11, and while Van Pelt birdied three of the next four holes to trim his deficit, it wasn't enough.
Donald gave Piercy all the encouragement he needed by double-bogeying the opening hole – Piercy won the first three – but losing the fifth had nothing to do with what the world No.3 did – Piercy sank his approach for an eagle two.
That gave him a 4-up advantage and from there Donald never really stood a chance.
Following Wednesday's freakish snowstorm and then the loss of Thursday morning as well, it was decided to play only the second round yesterday and then try to cram the last 16 and quarter-finals into today.