Brancalion wobbled again in the fourth with Cleverly's straight right hand and powerful left again doing the damage, but the Welshman also varied his attacks by utilising the uppercut, a shot that has proved so successful for him in the past.
Two fierce looping rights at the end of the round floored Brancalion, who received a mandatory eight count but was ultimately saved by the bell.
More punishment followed in the fifth, with two rights over the top again wobbling Brancalion, and with nothing coming back from the 34-year-old the fight was rightly stopped by referee Jean-Louis Legland one minute and 15 seconds into the round.
Cleverly can now add the European belt to his British and Commonwealth titles as he moves closer to a world title shot.
The Cefn Forest man added: "It's a long time coming to be honest.
"I've been waiting for this moment since 5 December when the fight was originally supposed to happen.
"The Italians messed us about a little bit but [promoter] Frank [Warren] delivered tonight and I did too, so I'm delighted.
"I had a plan going into the fight because British fighters are rough and tough and like a brawl but this guy is a European operator and stood off.
"So I had to pick my shots and in the end it was a comfortable night. I didn't pick up the pace because I didn't need to - I just counter-punched."
A former student at Enzo Calzaghe's world-renowned gym, Cleverly becomes only the seventh Welshman to hold all three belts.
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