Eto'o put the Spanish champions ahead in the 10th-minute at the Stadio Olimpico and Messi's 70th-minute header — his ninth Champions League goal of the season — sealed the victory as Barcelona won Europe's most prestigious club championship for the third time.
The victory over the defending champions completed a sweep of titles for 38-year-old Barcelona coach Pep Guardiola in his first season after wins in the Spanish league and cup.
United had been chasing its fourth European Cup title, and fourth trophy this season after winning the Premier League, FIFA Club World Cup and League Cup.
United was thoroughly outplayed by the Spanish side as Messi scored his 38th goal of an amazing year for Barcelona, which has scored 153 league and cup goals this season. Wednesday's looping header left Messi with two more goals than anyone else in the Champions League this season.
The loss left Man United manager Alex Ferguson at 25 titles in 23 seasons. He failed to match Liverpool's Bob Paisley's three titles in the competition.
South Korean winger Park Ji-sung made European football history by becoming the first Asian to play in a Champions League final. He almost scored for United in the opening minute but his shot was deflected wide after Cristiano Ronaldo's free kick had been blocked by the goalkeeper. It was the nearest United came to scoring all night.
The victory also marked the first Champions League title for French striker Thierry Henry, who was on the losing side when Arsenal lost to Barcelona in 2006.