Rooney, who was named player of the tournament, took a pass from Cristiano Ronaldo in the 73rd minute and fired an angled right-footed blast into the bottom corner past diving Liga goalkeeper Jose Cevallos.
"It was a very difficult game especially after going down to 10 men," said Rooney. "I'm very happy to have scored and for us to become the best club in the world is something we can be very proud of."
United was reduced to 10 men when defender Nemanja Vidic was given a red card in the 49th minute for elbowing Claudio Bieler in the face.
United becomes the first English club to win the cup in its current format. The Red Devils participated in the first Club World Cup in 2000 without making the final, while Liverpool lost the 2005 decider.
In 1999, United did win the predecessor to the Club World Cup, the Intercontinental Cup which matched the European and South American champions.
United manager Alex Ferguson had high praise for Rooney.
"He played well enough to score two or three goals tonight," said Ferguson. "It was a magnificent game that he played."
Liga didn't have a shot on target until Alejandro Manso rifled a left-foot blast from the top of the area in the 63rd minute only to see United keeper Edwin Van Der Sar make a spectacular diving save.
Manso came dangerously close to equalizing in the 89th minute with a long-range shot that Van Der Sar tipped over the bar.
Now we can say we are the best team in the world," said United captain Rio Ferdinand. "We knew they could create problems but I think today we kept them down to a minimum of chances."
Looking to add to their Premier League and Champions League titles, United controlled the flow of play from the outset.
Rooney had a superb chance 10 minutes in when he played a long ball from Vidic off his chest and unleashed a powerful volley from the top of the area that Cevallos stopped with a diving save.
Ronaldo set up Carlos Tevez 10 minutes later with a cross but the Argentine's low header was saved by Cevallos, who kept his team in the match in the first half.
Rooney set up Park Ji-sung after a nifty one-two with Tevez but the South Korean fired into the hands of Cevallos late in the first half.
Jairo Campos had Liga's best scoring chance in the opening minutes when he redirected a Manso free kick inches wide of the post.
United qualified for the Club World Cup in May after beating fellow English side Chelsea in a penalty shootout in the Champions League final at Moscow.
Liga qualified for the competition by becoming the first Ecuadorean club to win South America's Copa Libertadores.
Liga defeated Mexico's Pachuca 2-0 on Wednesday to reach Sunday's final, while United advanced after a 5-3 win over Japan's Gamba Osaka.
Gamba secured a third-place finish earlier Sunday with a 1-0 win over Pachuca.
Striker Masato Yamazaki scored the winner in the 30th minute when he volleyed a superb pass from fellow forward Ryuji Bando past goalkeeper Miguel Calero.
I NEVER fail, i'm just SUCCESSFUL in finding out what doesn't work Freedom is never voluntarily given by the oppressor; it must be demanded by the oppressed.