The winger, who was banned for three games for spitting at Manchester City goalkeeper Joe Hart, climbed above Angel Rangel at the back post to head the game's only goal past Michel Vorm on 39 minutes.
The Tigers are now nine points clear of the relegation zone with five games of the season remaining, while Swansea are three points further back and do not have enough to feel completely safe just yet.
Below, Sports Mole analyses whether the result was reflective of the action on Humberside.
On target: 4
On target: 2
Was the result fair?
Swansea had as many chances as Hull did when the scores were goalless, although they did not test the goalkeeper as severely as they would liked to have done. After conceding, they had the half-time break to regroup, but were flat in the second period and rarely threatened Hull's deserved lead.
Without Tom Huddlestone this afternoon, Hull needed other players to supply the strikers and Bruce allowed for this with a change in shape, opting for a 4-4-2 formation compared to the 3-5-2 system that he often uses. With two threats on each flank, the Tigers crossed very well all game, particularly from the left wing, and could have had more joy had it not been for good Swansea defending. Their willingness to deliver the ball early into the box was in stark contrast to the approach of Swansea, and Boyd's goal is evidence of what tact was more effective today. Curtis Davies and James Chester struggled to get in front of the powerful Wilfried Bony, but never allowed themselves to be isolated against the Ivorian in advanced areas, as Hull showed again that they are a well-organised and brave defensive unit.
Wayne Routledge started the game very brightly, supporting the claims made by Garry Monk that he is playing the best football of his career. He created chances for himself and Jonathan de Guzman in the opening stages, but then saw less and less of the ball. Bony's hold up play was again good, but he drifted in and out of the game and lacked composure in front of goal today. In a solid defensive display, Chico Flores and Ashley Williams dealt well with the succession of dangerous Hull crosses that were whipped so accurately into the Swansea box. What will annoy Monk is how their passing game was often slow and played in the wrong areas. They spent too much time on the halfway line and deeper, and instead could have taken a more direct route, using Routledge's pace and Bony's strength earlier than they did.
Sports Mole's man of the match
George Boyd: The former Peterborough United man may not have even been in the Hull team today had it not been for an injury to Huddlestone, but he certainly took his opportunity with both hands. In a slight change of system, Boyd offered the Tigers a natural source of width on the left flank, from where his delivery was always excellent. He was also not afraid to drift from his position to get involved in play centrally, as he did to great affect when scoring. Steve Bruce said this week that Boyd was "keen to make up for lost time" after completing his ban, and that was clear in his desire to collect the ball at every opportunity. He was difficult for Swansea to maintain and gave Rangel a very difficult afternoon.
Rangel and Vorm were left staring at each other following Boyd's goal. The Swansea full-back cowered under the aerial challenge from Ahmed Elmohamady's cross, but, equally, the ball was in the air for a long time and a keeper of Vorm's experience and confidence should have come off his line to claim.
Howard Webb must have woken up on the right side of bed this morning, seemingly deciding that there was little point in sending off Jonjo Shelvey for a second bookable offence in stoppage time, when the midfielder had clearly gone through the back of Robert Koren. Apart from that, the officials did not have any big decisions to make. Swansea may argue that a few minor went the way of the home side.
Hull: Steve Bruce's men can now focus on their first FA Cup semi-final since 1930, and only League One Sheffield United next weekend stand in their way of further progression in the competition.
Swansea: Swansea are winless on the road since November, so will be glad to be back on home soil next Sunday. Mind you, it is title-chasing Chelsea who are visiting the Liberty Stadium.