The visitors opened the scoring early on with a goal of pure class - Jay Simpson and Sone Aluko combining superbly before the latter applied the finish.
Steven Davies pulled the hosts level midway through the first half, before some calamitous defending allowed Stephen Quinn to poke home a winner for Hull shortly after the hour mark.
The Robins started brightly, but it was Hull who had the first opportunity of the match - Robert Koren striking a 25-yard free-kick straight at the hosts' wall.
But it wasn't long before the Tigers were ahead. Aluko and Simpson linked on eight minutes, exchanging a series of short passes on the edge of the penalty area, before Aluko found the space to fire the ball past Tom Heaton in the Bristol City goal.
Steve Bruce's men - sporting charity moustaches on their shirts for the trip to the south-west - continued to enjoy the lion's share of possession in the opening 20 minutes, looking comfortable as they stroked the ball around the pitch.
However, the hosts began to find their feet and were level on 25 minutes as Ryan Taylor sent a pin-point pass through for Stephen Pearson, who pulled it back for an advancing Davies, who duly smashed it into the back of the net.
Aluko went close to doubling his tally for Hull in the 28th minute, but was unable to direct his close-range effort at goal, sending it wide of the left-hand post.
The encounter became a much more even affair after the equaliser, with both teams taking it in turn to go on the attack - Simpson squandering a great opportunity to re-establish Hull's lead shortly before half-time.
Bristol City went close to grabbing a goal just after the break when a teasing Taylor ball into the area narrowly evaded the outstretched foot of goalscorer Davies.
Koren then had Ben Amos' bar shaking just a few minutes later when his 25-yard thunderbolt crashed against the woodwork.
The Tigers regained the lead on 65 minutes. After pulling off a superb save from an Aluko strike, confusion between Heaton and Cole Skuse left the hosts unable to deal with a soft attempt from Quinn, and the ball crept over the line with the help of Skuse's arm.
Simpson had the opportunity to all but seal victory in the 79th minute, but he dragged his effort wide of the left-hand post.
Despite efforts from the hosts to salvage something from the encounter, they were unable to find the back of the net, allowing Hull to take all three points.