Clarke is in 62nd place out of 64 in the American Express Championship at Mount Juliet in Kilkenny.
He came back from a bogey at the 12th with another birdie on the short 14th while Japanese playing partner Kenichi Kuboya dropped four shots in as many holes.
Montgomerie had another birdie himself on the 436-yard seventh, but four under par was still only good enough for a share of 36th place.
World number two Phil Mickelson had gone past him with three birdies in his first five holes, while Scott Verplank, another of Curtis Strange’s side at The Belfry, resumed with two birdies to go to six under.
Verplank, the one who said earlier this week that the Americans would all fly home if war with Iraq breaks out, then picked up another shot at the 402-yard fourth.