Appearing in their first ever major final, Hull rocked Arsenal by going 2-0 up inside just eight minutes through goals from centre-backs James Chester and Curtis Davies.
But Santi Cazorla’s sumptuous free-kick reduced the arrears in the 17th minute and after Laurent Koscielny netted an equaliser with 19 minutes of normal time remaining, Ramsey drilled home the winner in the extra period.
It was the Welsh midfielder’s 16th goal of a campaign that has seen him emerge as Arsenal’s most influential player and brought Arsene Wenger’s side a first trophy since the 2005 FA Cup.
Wenger, who is still to extend his contract, which expires shortly, has now won five FA Cups, while Arsenal have equalled Manchester United’s record of 11 successes in the competition.
Hull faded badly after their stunning start, but Steve Bruce’s side could console themselves with the knowledge that a Europa League place was already secure.
Chester had unexpectedly overcome a hamstring problem to take his place in Hull’s three-man defence, and nobody could have predicted how quickly he would have an impact on the game at a muggy Wembley Stadium.
Hull’s fans were still adjusting to the novelty of seeing their side in an FA Cup final when Chester put them ahead in the fourth minute, clipping the ball into the bottom-left corner from Tom Huddlestone’s mishit volley.
Huddlestone had been picked out by Stephen Quinn from a corner and four minutes later, Arsenal were again undone by a set-piece.
After Ahmed Elmohamady’s free-kick was partially cleared, Quinn put the ball into the box from the left and when Alex Bruce’s downward header came back off the post, Davies rattled the rebound home from a tight angle.