Hull recorded a second straight Premier League victory as a 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 over 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 for only his second Hull goal.
Hernandez then wrapped up the three points in stoppage time as the Swans were punished on the break.
Swansea had also won their first game at Burnley, but they ran out of ideas at the Liberty Stadium after a promising opening when Modou Barrow's pace had posed problems.
Hull win at Swansea thanks to late goals
