The USA took the lead once in the game in the final minute of extra time to finally overcome Canada 4-3 and a final meeting with Japan on Thursday.
An entertaining game at Old Trafford saw favourites USA three times fall behind to North American rivals Canada, before rallying in a frenetic second half which saw four goals in 12 minutes take the game to extra time.
Canadian skipper Christine Sinclair hit a hat-trick as the USA were caught out three times by breaks of their opponents despite dominating possession for long periods.
Canada only finished third in their group whilst the USA won all their group games, yet it was Canada who opened the scoring with their first real attack of note as Sinclair showed neat footwork inside the area to score and give her side a lead at the break.
For USA headers by Alex Morgan and Abby Wambach were the nearest the current Olympic Champions came to scoring.
But the US quickly restored parity just after the interval with Megan Rapinoe finding the net direct from a corner.
But Canada regained the lead through a Sinclair header only for the US to immediately level with a long range Rapinoe effort.
Another header gave Sinclair the match ball but a harsh penalty awarded when a fiercely struck free kick hit the hand of Lauren Sesselmann enabled leading scorer Wamach to level from the spot.
Both team`s then had opportunities to win the game in the final stages but extra time was needed and penalties was looking likely when Wamach heading against the woodwork.
But in the final minute of added time Alex Morgan rose highest to head home a dramatic winner and break Canadian hearts sending the USA into their fourth Olympic final and a meeting with Japan.
Referee: Christiana Pedersen (NOR)
Venue: Old Trafford
Canada scorers: Sinclair 20, 67, 72
USA scorers: Rapinoe 53, 70, Wamach pen 79, Morgan 120
Yellow cards: Scott (CAN), Tancredi (CAN)