Anthony Gordon was the star performer, scoring four goals, including two penalties, to achieve the first hat-trick of his senior career.
Gordon's first goal, scored within three minutes, surpassed Alan Shearer's club record of six goals in a single campaign.
Malick Thiaw and substitute Jacob Murphy also contributed to Newcastle's goal tally, while Elvin Jafarguliyev scored Qarabag's lone goal.
The comprehensive win puts Eddie Howe's side in a commanding position ahead of the second leg, virtually guaranteeing their progression to the last-16.
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