The midfielder, handed a three-game ban for spitting at Joe Hart in last month’s defeat to Manchester City, struck just before half-time to settle a nervy contest.
Swansea City responded by laying siege to the Tigers’ goal after half-time but they could not find a way past the resolute hosts.
It means Hull have claimed a tenth win of the season - the target Steve Bruce set his players back in August as a guarantee of avoiding relegation.
With five games remaining, it is a fine achievement and one that means City can go into next week’s all Yorkshire semi-final with Sheffield United without having to worry about what is happening in the league.
Hull wasted a great early chance when Maynor Figueroa picked out Shane Long with a pinpoint cross and the striker’s header was saved superbly by Michel Vorm.
The Swansea goalkeeper also saved smartly from george Boyd
Swansea also had opportunities in an open 45 minutes with Jonathan De Guzman wasting a glorious opening.
Released by a first time ball from Wayne Routledge, De Guzman seemed to have a clear run on goal only to slow down and be swamped by amber and black shirt. His shot was eventually blocked by Figueroa.
The Tigers had another let-off when Routledge chipped a shot straight into Steve Harper’s hands when more elevation would surely have beaten the veteran goalkeeper.
It proved a costly miss, with Hull going ahead six minutes before the break when Liam Rosenior picked out George Boyd with a deep cross that the former Peterborough man gleefully headed beyond Vorm.
Swansea, with Nathan Dyer brought off the bench during the interval., were the better side during the second half.
Jonjo Shelvey brought a save from Steve Harper, who was then relieved to see Dyer shoot wide after Hull had been opened up by Wayne Routledge.
With seven minutes remaining, Wilfried Bony wasted an excellent opening by firing wide