South Africa’s Ernie Els, twice a winner of this title, found sand at the third and dropped into the group on three over.
After both players parred the second, McDowell blinked first at the short third when he failed to get up and down from the front of the green.
At level par he was one behind the consistent Furyk, while Belgian Nicolas Colsaerts - who started the day two over - responded to four straight bogeys with a lengthy birdie putt at the fifth.
There was a hammer blow for Westwood at the fifth when his drive leaked right and lodged in a tree. The 39 year old borrowed some binoculars but couldn’t spot it and so it was declared lost. He returned to the tee and took four with his second ball, but that meant a double bogey six on the card and he dropped to four over.
There was better news for Ireland’s Padraig Harrington, who had three successive birdies from the seventh to be joint ninth at four over.
Els hit a three wood to 12 feet on the driveable seventh and holed the eagle putt, moving into a share of second as a result.
McDowell and Furyk both missed the green at the fifth, but while McDowell missed his curling six foot par effort, Furyk’s was never anywhere other than the middle of the hole.
The American led by two as a result, with five players four behind on three over in a share of fourth.
Harrington looked in trouble at the 13th after missing the green left but he chipped in and at two under for the day and three over for the week he was right back in the thick of it.