Last season's relegation play-off winners have drawn both of their games this term, with Kim netted a brace in their most recent stalemate - a 2-2 draw with third-placed Suwon Bluewings.
That denied Bluewings two wins from two and Sangju will aim to halt another 100 per cent record this week when Jeonbuk travel to the Sangju Stadium.
Jeonbuk have picked up wins against Busan I'Park and Incheon United this season, with Ulsan, the only other side to have won both games, hosting the latter on Sunday.
Last year's runners-up Ulsan have made a great start to their 2014 campaign, picking up wins over holders Pohang Steelers and Gyeongnam, with the form of Kim Shin-Wook a primary reason behind their success.
He has three goals in his last three games in all competitions after a tough schedule that also saw him visit Greece for a friendly with South Korea.
"More than my personal scoring streak, I am happy that our team has won four games in a row," Kim told the Yonhap news agency.
"I've been running on fumes since the game against Kawasaki Frontale last Wednesday, but the joy of victories has kept me going."
Reigning champions Pohang will look to kick-start their campaign after enduring a nightmare opening to their title defence.
Pohang sit rooted to the foot of the K-League ahead of their clash with Suwon, while Seongnam and Seoul can pick up their first league win at the weekend against Jeju United and Busan respectively.
