The Ukrainian champions need to deny City victory at the Metalist Stadium in Kharkiv on Wednesday to guarantee themselves a place in the last 16.
Teenager Phil Foden was given his full debut, becoming the youngest Englishman to start a UEFA Champions League game, with Gabriel Jesus, Leroy Sane, Ederson and Fernandinho the only regular starters included, and City's lack of cohesion proved costly.
For large periods on Sunday, however, City were frustrated by an organised West Ham but their sheer will to win proved too much for the Hammers as Guardiola's side restored their comfortable lead ahead of next weekend's Manchester derby.
Manchester City manager Pep Guardiola, in his post-match comment, said: "Today was different to (the late winning goal against) Southampton - I did not think that was going to happen".
But even that still isn't enough to make them firm favourites for when their rivals visit Old Trafford on Sunday. We are in a good moment.
"Our opponents have all these issues". No stories of (Alexandre) Lacazette, David Silva.
With the Premier League leaders already a goal down, Ederson misjudged a ball over the top from Shakhtar, allowing Ismaily the relatively straightforward task of scoring the home side's second of the night.
United fell behind late in the first half when Vitinho's shot from Mario Fernandes's cut-back struck team-mate Alan Dzagoev on its way into the net.
'I have had similar deciders in my career but this is the first time I have had such a game in the Champions League'.
With Mark Noble absent, Fernandes proved what he can alongside Pedro Obiang and Cheikhou Kouyate, and it is difficult to see Moyes moving away from that trio if they all remain fit and available.
And now, according to the Daily Mail, Mourinho is confident of landing the left-back for £50 million before the start of next season, either in January or over the summer.
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