Armed with last-rock advantage in the final end of a tied game against Scotland, the Ottawa skip missed a double takeout attempt and Eve Muirhead stole a point for a dramatic 8-7 semifinal victory.
"We played really well and we deserved the win," Homan said. "It's too bad it had to end that way but sometimes it happens."
Homan will have to settle for an appearance in Sunday's bronze-medal game against Erika Brown of the United States. Muirhead will play Sweden's Margaretha Sigfridsson for the gold.
The semifinal featured stellar shotmaking and plenty of offence. The few hundred fans in attendance at the Volvo Sports Center were treated to a back-and-forth affair that could have gone either way.
"Rachel threw a great attempt at the double but it just hung a little straight on her and they got the win," said Canadian coach Earle Morris.
Muirhead, a year younger than her 23-year-old counterpart and just as intense, shot 88 per cent on the game. Homan finished at 86 per cent.
The Scot opened with a takeout to score a pair. Homan answered with a draw to the button for a deuce of her own but Muirhead replied with two more points in the third end.
Homan hit a tapback for two to pull even in the fourth. After alternating singles, the Canadians scored a pair in the eighth for a 7-6 lead before Scotland tied it with a single in the ninth.
"It's one of the finest curling games I can ever remember our team being involved in," Morris said. "It was a battle. It was like a boxing match out there. Both teams played really well and made some big shots. It was the kind of game that I think deserved to have the last one made, whether it was Scotland throwing the last shot or Canada throwing the last rock.
"But it's why we play. You can't guarantee what the outcomes are going to be."
Canada hasn't won a world women's title since Jennifer Jones was victorious in 2008. Homan beat Jones last month at the Scotties Tournament of Hearts in Kingston, Ont., to qualify for the world championship.
Alberta's Heather Nedohin skipped Canada to a bronze medal at the 2012 event in Lethbridge. Switzerland's Mirjam Ott beat Sigfridsson in last year's championship game.
Earlier in the day, Homan defeated Brown 7-6 in the 3-4 Page playoff. The Canadians looked relaxed and confident in their first career world women's playoff game.
Homan opened the scoring with an impressive in-off for a deuce before the United States cut the lead in half with a takeout in the second end.
Homan scored two more in the third. The Ottawa skip took out a U.S. rock and it nudged another American stone just enough to give Canada a second point.
The United States followed with back-to-back singles, cutting Canada's lead to 4-3 at the halftime break. Homan tried a tapback in the fifth but just missed to give the Americans a steal of one.
Canada scored a deuce in the sixth end before the teams traded singles leading into the 10th, with Canada up 7-5. Homan had last rock and took out one of the American stones for the one-point win.
Canada leads all countries with 29 podium appearances in the tournament's 34-year history. Canada also leads with 15 gold medals, well ahead of second-place Sweden's eight.
Sigfridsson lost to Switzerland's Mirjam Ott in last year's championship game.
A group of flag-waving, cowbell-ringing Canadian fans took in the action from the front row of the 1,000-seat venue on Saturday. Small groups of American and Scottish fans were also on hand.
There were some unique touches at the host venue, about a 15-minute drive from the main drag of the Latvian capital.
The event MC did his best Bruce Buffer imitation by stretching out the surname of each curler during the pre-game player introductions. Once play started, the quiet vibe was interrupted during end breaks by blasts of thumping 80s-inspired mashup dance music selections.