It was an altogether different story for Leeds who looked a shadow of the side that had not lost in its previous six league and cup games.
They rarely threatened the home goal though Peter Schmeichel had to make a miracle save to keep out a deflected shot from Harry Kewell when the game was goalless.
Leeds manager Terry Venables was far from disheartened by the defeat and his sides display, claiming: " I was not to unhappy with our performance. We did alright in the first half and camped for much of the second in their half.
"Peter Schmeichel made a brilliant save to deny Harry Kewell and I feel we were a bit unfortunate to come away empty handed."
City broke the deadlock in 29th minute with a well-worked goal as Eyal Berkovic threaded a superb through ball for Goater to slot home his sixth goal of the season.
Danish international Jensen sealed victory early in the second half with a stunning goal, when he latched on to a Nicolas Anelka ball and unleashed an unstoppable volley form the edge of the penalty area.
City might have won by a wider margin but for two spectacular stops from Paul Robinson.
The young keeper made a miraculous stop to tip over from Kevin Horlock and then did well to keep out another long-range effort form Jensen.
True to style City didn't do it the easy way as they conceded a stoppage-time goal, scored by Kewell, that resulted in a nerve jangling final few seconds.