Johnson carded the best round of the group, as his 65 Saturday at Glen Abbey Golf Club will put him in the final pairing alongside An for Round 4.
Tway, the leader after 36 holes, held his ground in the third round, shooting 4-under to hold the lead after 54 holes for the first time of his career.
The leaders have a four-shot lead over the field, with one glaring difference between them. An, Kim, and Tway are all searching for their first PGA Tour win, while Johnson is looking for his third this season alone.
Mackenzie Hughes is the low Canadian heading into the final round after he birdied five of his final six holes, shooting 67 to come in at 11-under for the tournament.
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