While Chelsea kept alive its faint hopes of retaining the Premier League title with a 3-1 win at West Bromwich Albion, City midfielder Yaya Toure scored a 52nd-minute winner to leave United with the domestic championship and Champions League to aim for.
City, which is fourth in the Premier League and on course to qualify for next year's Champions League, plays either Stoke or Bolton in the May 14 final — when it aims to break a 35-year streak without a trophy.
"We've done nothing yet," City goalkeeper Joe Hart said. "We've got ourselves into a good position in the league and we've put ourselves in the final. Nothing's been won yet."
Toure scored after intercepting a poor clearance by United midfielder Michael Carrick and United ended with 10 men after Paul Scholes' 72nd-minute red card for a dangerous lunge on Pablo Zabaleta.
City had been overrun for most of the first half and Dimitar Berbatov should have put United ahead, but had one shot blocked by Hart and put another over the bar from close range in front of an unguarded net.
Backed by an investment of about $1 billion by owner Sheikh Mansour since 2008, City now has a shot at a first trophy since the 1976 League Cup. It reached the 1981 FA Cup final, but lost a replay to Tottenham.
"The boys are over the moon, the club are over the moon," Hart said.
United was without the suspended Wayne Rooney and left Javier Hernandez, who scored in Tuesday's Champions League victory over Chelsea, on the bench. Considering Berbatov's wayward finishing, the selection may have been an error.
