Two goals from Dejan Damjanovic did the damage as the defending champions moved up to seventh place in the table.
The Montenegrin marksman put Seoul ahead after eight minutes, turning in a smart pass from Mauricio Molina, before then heading home in the 29th minute to put the visitors in control.
Koh Moo-yeol pulled a goal back for Pohang ten minutes before the interval but the hosts were unable to get the all-important equaliser.
"Dejan is a top class striker," said Seoul caretaker-coach Choi Yong-soo.
"He was well-supported by his team-mates. We showed our fighting spirit and kept going until the end."
Pohang coach Hwang Sun-hong remained upbeat despite the loss.
"We missed the chance to close the gap with Jeonbuk, but we played with passion," he said.
"There is still a long way to go this season and lots of points still to play for."
Chunnam Dragons moved into third with a 3-1 win at home to Daegu FC.
Kim Myong-joong put the hosts ahead in the opening minute only for Sung Jae-han to equalise for Daegu eight minutes before the interval.
Shin Yong-joon then restored Chunnam's lead ten minutes after the restart before Javier Reina made sure of the points with a last-minute penalty.