Pep Guardiola's visitors were far from their free-flowing best en route to their 12th win of the season, but were nevertheless good value for a win that keeps them seven points behind leaders Chelsea.
Yaya Toure's penalty, awarded after Andrew Robertson's clumsy challenge on Raheem Sterling, set the visitors on their way before Kelechi Iheanacho added a second from close range and Curtis Davies conceded an own goal in the dying seconds.
Hull have now conceded nine penalties so far in the league this season - four more than any other side.
The hosts played well in patches and saw Michael Dawson's second-half header cleared off the line by Bacary Sagna, but their return of one win in 16 matches is a damning statistic that points to only one outcome come season's end.
And it will not be lost on Tigers fans that the side bottom on Christmas Day have only stayed up three times in the 24 Premier League seasons to date.