The Argentine forward, playing for the first time since the Christmas break, also hit the crossbar in a display so impressive that even many of the Atletico fans stood and applauded him when he was replaced near the end.
Barcelona made most of the early running at a chilly Vicente Calderon despite resting key players from the team who beat Real Mallorca at the weekend, including Xavi and Samuel Eto'o.
A deft piece of skill from Daniel Alves unlocked the Atletico defence for Messi's opening goal on 12 minutes.
The Argentine international played the ball inside and Alves sent a clever backheel through for him to run on and place a low shot past Gregory Coupet.
Atletico had to play with 10 men for most of the second half after defender John Heitinga felled Messi in the penalty area as he was racing to meet an Alves cross.
The referee showed the Dutchman a red card and Messi sent Coupet the wrong way to double Barca's lead.
Atletico substitute Tomas Ujfalusi pulled a goal back just over 10 minutes later with a header from Simao Sabrosa's corner, but the margin was restored when Messi completed his hat-trick on 80 minutes.
Copa del Rey last-16 fixtures - Wednesday
Sporting Gijon v Real Valladolid
Sevilla v Deportivo Coruna
Racing Santander v Valencia
Real Union de Irun v Real Betis
Ejido v Espanyol
Copa del Rey last-16 fixtures - Thursday
Osasuna v Athletic Bilbao
Real Mallorca v Almeria
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