With a shot from behind a tree, Cameron Smith, one of six players who recently joined the Saudi-funded league, saved par, and he finished with a 45-foot eagle putt for a 64.
A 64 was also shot by Joaquin Niemann of Chile, who signed with Greg Norman's league after the Tour Championship ended his PGA Tour season.
A number of newcomers were highlighted by Smith and Niemann, including Anirban Lahiri (66), Harold Varner III (67), Marc Leishman (70) and Cameron Tringale (71).
Wolff made his fifth ace of the round on the 178-yard second hole. In the fourth LIV Golf Invitational series, the ball took one hop and disappeared into the cup
Aside from six birdies, the former Oklahoma State star had another eagle on the par-5 12th hole. It was enough to offset three bogeys and give him the lead.
The group included Lahiri and Louis Oosthuizen at 66, while Johnson was at 67. Despite finishing in the top 10 in previous LIV events, Johnson has yet to win.
Only 12 of the 48 players failed to post par or better at The International, about 45 minutes west of Boston. Among them was Phil Mickelson, who shot 74.
Piot, the former U.S. Amateur champion, shot 77, but Kim had a rough day. In addition to four double bogeys, Kim shot 87 after taking a 10 on the 16th hole.