An own goal and a goal from Ianis Hagi put Steven Gerrard's side in control and they held on despite having Ryan Kent sent off just before half-time.
In the same stadium earlier in the evening, Celtic drew 1-1 with Nice - Patryk Klimala was on target for Neil Lennon's team.
The next games are on Saturday when Celtic face Lyon and Rangers take on Nice - both fixtures will again be played in the Groupama Stadium.
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