Sydney, who haven't won their last eight A-League matches, dating back to their 2-1 win over Western Sydney Wanderers on 16 January, produced a strong first-half performance and were ultimately rewarded through Chris Naumoff in the 42nd minute.
A clever George Blackwood through ball found Naumoff, whose sliding finish, from an acute angle, beat Pohang goalkeeper Shin Hwa-yong and gave the visitors an unlikely lead.
It was the first goal the South Korean outfit had conceded in their last six Champions League matches.
For the Sky Blues, who hadn't won outside New South Wales all A-League season, the victory over the 2009 Champions League winners continues their strong ACL form after a last up home win over reigning champions, Guangzhou Evergrande.
Just eight minutes after half-time, Graham Arnold's men almost doubled their lead through Naumoff, but his shot was desperately cleared off the line by Pohang defender Gwang-Seok Kim before Sydney's Andrew Hoole blazed over the bar.
While the K League side, who finished last season's domestic league in third place, pushed hard for an equaliser at stages during the second-half, Sydney were resolute in defence and held on for a valuable three points on the road.