Donald needs to finish in the top eight at Harbour Town - where he lost a play-off to Brandt Snedeker last year - to remain ahead of Ryder Cup team-mate Rory McIlroy in the rankings.
But the Englishman struggled to a four-over par 75 to lie seven shots off the early clubhouse lead held by Jim Furyk.
Starting from the 10th, Donald dropped shots at the 12th and 15th to reach the turn in 37.
He then recovered from a bogey on the first with a birdie on the par-five second, but ran up a double-bogey six on the sixth to continue the disappointing form shown at last week's Masters.
Ireland's Padraig Harrington, who enjoyed a return to form when finishing joint eighth at Augusta, fared only marginally better than Donald with an opening 74.
The triple major winner carded four bogeys and just one birdie as the tight course made low scoring difficult.
Furyk's round of 68 featured five birdies and two bogeys, but was enough for a one-shot clubhouse lead over fellow American Blake Adams.
"It feels very good," the 2010 winner told PGA Tour Radio. "I checked the weather last night, it was going to be cold and gusty and windy and the forecast was spot-on.
"That first nine played very difficult so to get out to a decent start I am very happy with my score.
"It will be one of the better scores in the morning, I'm sure the scores will get a little better in the afternoon, but it will keep me in the tournament."