Strikes either side of the half-time whistle from Stina Blackstenius and a goal by Lina Hurtig proved the difference as Sweden claimed a famous triumph over their heavyweight rivals, who they defeated on penalties in the 2016 quarter-finals.
The world champions enjoyed a two-year spell without losing before the Group G opener but will quickly have to bounce back if they are to follow up their France 2019 success with Olympic gold.
Rapinoe found it hard to defend the USA's performance as she credited Sweden's hard-working display.
"We did not play a very good game and that is to take nothing away from Sweden, they played a great game," the attacking midfielder said after the match.
"This is the highest level and these are the best teams in the world. Sweden are one of the best ever in Europe and the world. If we don't play well we don’t win these games.
"We want to be a lot better, we played a bit tight and hurt ourselves a lot. You can't say one thing specifically.
"I can't remember the last time we gave up a goal, so to give up three is not great but we know what we need to do to win these games, get out of the group and go from there."
Head coach Vlatko Andonovski refused to panic and is keen to see a response against New Zealand on Saturday.
"It has put us in a big hole and we are the only ones who can get ourselves out of it," he said. "It is not going to be easy. We have to get good results in the next two games, but I know this team will not give up.
"I don’t remember this team losing 3-0 in recent history so it is a bit of a shock, but everyone is positive. We still have games ahead of us. We have got to bounce back. We have to forget this game and focus on the next one."
In contrast, Blackstenius, whose brace sealed a remarkable victory, spoke glowingly of her team, who were without Chelsea captain Magdalena Eriksson for the win.
"I'm very happy about the goals - of course I'm happy to score. The team helped me very much and I think I could have scored at least two more but I don't want to focus on that. I'm just happy and proud of the team", the forward said.
“We developed our game and our play. It's very good and we have so much quality in every player. Every player is also very different from the other. We have so many players that can do good stuff and as a team we are very good. Every player is very happy about going very attacking."
Hedvig Lindahl, though, maintained that Sweden's win was simply a starting point and that Peter Gerhardsson's side had not achieved what they had come to the Games for yet.
"It's just the first group game, we haven't won anything yet. We need to keep going," the veteran goalkeeper said. "If you have one high into lows in the group then this means nothing. But to win against the USA, it's something we can take some confidence from.
"You can go very far in a tournament even if you lose to the USA or whoever you play in the first game, so I don't know how much it means, but we showed the world and ourselves that we can play good against a team like the US and any team."
The USA came into the Games as firm favourites for the gold medal, but Sweden offered a rude awakening for the reigning world champions. They had previously not been defeated since back in 2019 before that run was ended by their emphatic setback in the Group G opener.
Goals either side of half-time from Stina Blackstenius and another from Lina Hurtig did the damage, and while the USA were denied twice by the woodwork, Sweden were deserved winners to repeat their quarter-final shoot-out victory over the same opposition at Rio 2016.
In fact, Sweden's three-goal win was the first time since 2008 that the USA have lost in a major tournament by multiple goals and only the sixth time in their history that they have lost a game by three or more goals.
While the USA struggled, Brazil gave an early signal of their intent. Marta's opener made her the first player, male or female, to score at five consecutive Games, while the 35-year-old also moved to second in the all-time top scorer list at the Olympics.
The Brazil forward's record-breaking outing in Group F stole the headlines, but 43-year-old Formiga made history herself. She became the first women's footballer to appear in seven editions of the Games, and is hoping to become the oldest female representing Brazil to claim an Olympic medal, a record previously held by 38-year-old volleyball star Fofao.
In more routine fashion, Great Britain got off to a strong Group E start as they cruised past Chile 2-0, with Ellen White netting both goals.
White spoke of her pride after the win and credited her team-mates who provided the chances for her brace.
"I'm obviously delighted to contribute to the team winning, to score two goals. I feel really proud to open the Olympics with Team GB," the forward said.
"It was a great header down from Lauren Hemp for the first one and an amazing cross from Lucy Bronze for the second.
"We've been working really hard to get to this point. I feel really delighted with where I'm at the moment, but I feel there's still more to come. Collectively as a squad we [can] grow and get better as the tournament goes on."
Team GB and Chile both took the knee, as did the USA and Sweden in their fixture, as athletes across the globe continue to make a stand against racism.
Meanwhile, Barbra Banda announced herself on the world stage with a hat-trick, despite Zambia going down 10-3 to the Netherlands.
The Netherlands led 6-1 at half-time following Vivianne Miedema's hat-trick and a brace from Lieke Martens.
Sarina Wiegman’s side then added four more goals in the second half, with Miedema getting a fourth, before Banda hit back twice in the final 10 minutes.
The 25-year-old stormed to victory ahead of Canada's Marielle Thompson, with Daniela Maier claiming bronze after Marielle Thompson was bumped down for an infringement.
Naeslund joins Thompson and Jean-Frederic Chapius as the only freestyle skiers to have won Olympic gold, the world championship title and the crystal globe in the event.
Canada have won a medal in all four Games this event has been held, though unlike in 2010, 2014 and 2018, they were unable to stand top of the podium.
Stats Perform picks out some other standout numbers from Thursday's action in Beijing.
7 - Japan's Miho Takagi won her seventh Olympic medal with victory in the women's speed skating 1000m, surpassing China's Wang Meng (six) for the most medals won by an Olympian representing an Asian nation in the Winter Games.
12 - Brittany Bowe claimed bronze in the same event to make it 12 medals for the United States in the women's 1000m, followed by 10 for the Netherlands, who won silver thanks to Jutta Leerdam.
3 - Switzerland's Michelle Gisin became the third athlete to defend her Olympic title in the women's alpine combined after Janica Kostelic in 2002 and 2006 and Maria Hofl-Riesch in 2010 and 2014.
5 - Gisin's team-mate Wendy Holdener won silver for her fifth Olympic medal as Switzerland achieved a gold-silver finish in a women's alpine skiing event at the Winter Games for a third time, previously doing so in the 1956 downhill and 1984 downhill.
7 - Canada prevailed 3-2 winners against the USA in the women's ice hockey final to win their fifth gold medal since its introduction to the Games in 1998. This was the seventh medal in event for both nations, having each made the podium every year the event has been contested.
4 - With two goals on Thursday, Canada's Marie-Phillip Poulin is the only ice hockey player – male or female – to score in four Olympic Games finals, scoring seven times in total across those games.
17 - Anna Shcherbakova and Alexandra Trusova, both 17 years old, won gold and silver respectively in the women's single figure skating, marking the first time that multiple figure skaters under the age of 18 finished on the podium of the event since 1998 when American duo Tara Lipinski (15) and Michelle Kwan (17) won gold and silver respectively.
