The former England international netted in the 48th and 77th minutes while also providing the assist for Lucas Silva's 61st-minute header as the South Korean side picked up their second win in the eastern league phase of the competition.
"It's important," the 32-year-old Lingard said of the victory. "Any Champions League game, we know it's going to be a big game on the big stage.
"We had a different game plan and it worked, the manager stuck to the game plan, the players stuck to the game plan and we got the win in the end."
Lingard gave FC Seoul the lead following Marko Dugandzic's layoff but Mateus Vital levelled the scores nine minutes later with a stunning strike from distance.
Lucas Silva restored his side's lead when he glanced Lingard's cross past goalkeeper Yan Junling and the ex-Manchester United forward then sealed the win with a first-time finish.
The win moves FC Seoul up to fourth in the 12-team standings after five matches, with the top eight finishers progressing to March's Round of 16 phase. The quarter-finals, semis and final will be played in Saudi Arabia in April.
Melbourne City pulled level on nine points with eastern league phase leaders Vissel Kobe, who play Shanghai Shenhua on Wednesday, as Aurelio Vidmar's side secured a 2-0 victory over Malaysia's Johor Darul Ta'zim.
Max Caputo headed in a third-minute opener while substitute Medin Memeti scored a second in stoppage time to give the Australian side their third win in a row in the competition.
Japan's Machida Zelvia sit third on eight points after a 3-1 win over Gangwon FC from South Korea with first-half goals from Keiya Sento, Hokuto Shimoda and Oh Se-hun earning the points for Go Kuroda's side.
Sanfrecce Hiroshima are fifth having drawn 1-1 with Chengdu Rongcheng in China as Mitsuki Kato scored in the 63rd minute to cancel out Felipe's 54th-minute opener from the penalty spot.