However, after a nervy opening half hour, Fulham comprehensively outplayed FC Vetra, who finished third in the A Lyga last season.
Brede Hangeland nodded a corner wide, Zamora shot straight at keeper Povilas Valincius and Zoltan Gera flashed wide of the near post as the Cottagers failed to turn their increasing dominance into goals.
Zamora settled any nerves, though, when he fired in a delicious opener moments before half-time.
And Murphy effectively killed the game off from the spot 10 minutes after the restart after Zamora had been hauled down by Vetra skipper Algis Jankauskas.
From then on the match resembled a training ground exercise as the Londoners controlled the tempo and frustrated their opponents.
But there was still time for Seol to complete the scoring, the South Korean drilling into the corner after more good work from Zamora.
Afterwards, Zamora told Fulham's website: "It was important for us to start with a win. We're all loving playing in Europe - we're going to relish every minute of it.
"Now we're just looking forward to the second leg next week. It'll be another tough workout for us and hopefully we'll come out of it with another win.
"They were organised and they worked hard. They put the ball in the box and they'll give us another hard game back at the Cottage next week."
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