Morocco forward Ziyech grabbed his first goal since October to put the hosts ahead in the first half at Stamford Bridge.
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Liverpool have started with six wins in the Premier League and a victory in the Champions League but they were knocked out by a superb solo goal from Hazard in the 85th minute.
The draw, held in Nassau, Bahamas, revealed that Nigeria will play Italy, while the hosts Bahamas will face Switzerland in their opening matches of the competition on April 27