The Spaniard suffered his biggest-ever defeat in league football after they had enjoyed the lion's share of possession and chances but paid for sloppy defending that led to the Belgian powerhouse Lukaku converting his 12th league goal of the season after 34 minutes.
Guardiola gets first taste of FA Cup
Kevin Mirallas struck right after the break and excellent 18-year-old academy graduate Davies dinked a brilliant first goal for his boyhood club as City looked increasingly clueless.
Substitute Lookman, making his debut at 19, then completed the rout with his first touch in stoppage time, a goal that stemmed from a mistake from Everton old boy John Stones as City suffered a fourth league defeat in their last eight league matches.
Guardiola all but gives up on league title
Coming hot on the heels of their last loss in Merseyside at Liverpool on New Year's Eve, City were left in fifth place, now 10 points adrift of leaders Chelsea, as Guardiola cut a forlorn figure on the bench.
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