The Premiership side were in control thanks to a Billy Twelvetrees try and 14 points from the boot of former Edinburgh scrumhalf Greig Laidlaw but some ill-discipline nearly allowed the Scottish team to snatch an unlikely victory.
Gloucester were 19-6 to the good just before the hour mark when flanker Ross Moriarty was yellow-carded for recklessly putting his knee into the back of prone Edinburgh lock Fraser McKenzie at a scrum.
Re-energised Edinburgh then began to drive forward and Gloucester were reduced to 13 men when Billy Meakes was red-carded for a high tackle on Sam Beard.
With Meakes close to tears in the stand, Ross Ford touched down and Sam Hidalgo-Clyne kicked the conversion to leave Edinburgh needing a converted try to win the competition for the first time.
Despite some intense late pressure from the opposition, Gloucester held firm to lift their first European trophy for nine years.
"Things didn't go our way in the second half but we stuck to our plans and got the result," Gloucester captain Twelvetrees said.
(Writingn by Martyn Herman, editing by Tony Jimenez)
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