Hull recorded a second straight Premier League victory as their 2-0 win condemned Swansea to a first home defeat since February.
Shaun Maloney and Abel Hernandez struck in the final 12 minutes as the Tigers built on their surprise opening day win at home to champions Leicester.
Maloney had only been on the pitch six minutes when Curtis Davies flicked on Robert Snodgrass' 78th-minute corner and he finished from close range.
Hernandez wrapped up the three points in stoppage time as the Swans were punished on the break.
Swansea had won their first game at Burnley, but they ran out of ideas at the Liberty Stadium after a promising opening in which Modou Barrow's pace posed problems.
Until Maloney's goal it looked as if the main talking point would be referee Stuart Attwell turning down three penalty claims in the first half -- two from Swansea and one for Hull.
Barrow appeared to be taken out by Tigers defender Andrew Robertson after 14 minutes, even though the Swansea winger was running out of room in the area.
Five minutes later, Leroy Fer fired at goal but Tom Huddlestone came in late and made contact with the Swansea midfielder after the ball had gone.
The hosts might have had cause to feel aggrieved that their claims were ignored on both occasions, but Hull seemed to have a more cast-iron case four minutes before the break.
A Snodgrass run across the area was ended by Jordi Amat's sliding tackle, but again Attwell waved play on even though the Spaniard appeared to make no contact with the ball.
Swansea might have been celebrating a goal inside six minutes when Wayne Routledge laid Kyle Naughton's cross into the path of Gylfi Sigurdsson.
The Iceland international made a sweet connection and the ball seemed destined for the top corner before Eldin Jakupovic tipped it onto the crossbar.
That early chance set the tone for an open contest in which Hull were content to sit and break at speed.
After Barrow's penalty appeal was refused, Snodgrass set up Adama Diomande and the striker was thwarted by Amat's last-gasp challenge.
Barrow freed Routledge and his cross was met by Fernando Llorente, but the Spaniard failed to keep his header down from 10 yards.
Swansea were becoming increasingly frustrated in their struggle to create chances and it was showing in the theatrical response of manager Franceso Guidolin in the technical area.
Davies almost put the ball into his own net when Sigurdsson's corner was allowed to travel across the six-yard box.
But the central defender soon left his mark in the Swansea area -- and Hull were on their way to making it six points out of six.