Liverpool recovered from going a goal behind to beat Bordeaux 2-1 at Anfield to move to the top of Group B with goals from James Milner and Christian Benteke.
Harry Kane's late goal helped Spurs to a 1-0 win over their hosts, Qarabag in Azerbaijan.
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But Celtic will finish at the bottom of Group A after they allowed a lead to slip as Ajax claimed a 2-1 win at Parkhead.