The hosts, who won the Turkish Super Lig title last season, got off to the best possible start when former Chelsea striker Demba Ba sprinted from the half-way line to finish past Dean Henderson.
United's defensive frailties continued when Juan Mata was dispossessed by Deniz Turuc, who then set-up Edin Visca to fire home Basaksehir's second.
But United failed to lift in the second-half as they accepted their first loss in the Champions League this season.
It was another desperately poor performance from United, who put in a similar showing in the loss to Arsenal last weekend.
The loss means United will now have to work hard to secure their place in the knockout stages.
RB Leipzig and PSG meet later on Wednesday, a win for either side would put them level on points with United.
For the Red Devils, they must work to shore up their defence ahead of Saturday's clash with Everton at Goodison Park.
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