The American win was the major upset on a day that saw defending champion the Netherlands struggle to a 3-2 win over Japan and hosts Britain prevail 5-3 in an eight-goal thriller with South Korea.
While the American win was a major surprise, it was not unprecedented.
The United States got into the Olympics by beating Argentina 4-2 in last year's final at the Pan American Games — which was considered the best win in U.S. field hockey history at the time.
On Tuesday they showed it was no fluke.
Taylor got behind the Argentine defence and tipped a ball played by Michelle Vittese into the roof of the net shortly before halftime, giving goalkeeper Florencia Mutio no chance.
The Americans controlled long stretches of play against the No. 2-ranked team in the world by keeping Argentine star Luciana Aymar largely silent throughout.
"We don't like the way they play, its very physical. They foul a lot," Aymar said. "Sometimes it feels like they don't want to play."
U.S. captain Lauren Crandall said her team set out to neutralize Aymar.
"We put our best defender on her. Aymar is the best in the world," she said. "Every team has a best player and if you don't watch them, they might not have the ball for 69 minutes, but in the last minute they score a goal."
Both teams are now 1-1 in Group B play.
Earlier, Kim Lammers took her tournament tally at her first Olympic tournament to four goals in two matches as the Netherlands beat Japan 3-2 and Britain scored twice late in its match with South Korea.
The British victory moved the hosts to the top of Group A on goal difference.
Lammers scored in each half for the Dutch and Ellen Hoog smashed in a powerful backhand shot to give the Netherlands a comfortable-looking 3-0 lead early in the second half.
But Japan fought back when Rika Komazawa, who had to leave the pitch in the first half after being hit in the face by a stick, scored in the 45th minute. Japan drew closer when Aki Mitsuhashi deflected a penalty into the Dutch net seven minutes later.
Hoog said there was room for improvement for the defending champion.
"We are satisfied with the two wins and six points, but today we were not very good so we have things we can work on," she said. "We were not playing together and as a team, and we were not very sharp."
Komazawa said her team was ruing not taking the game to the Dutch earlier.
"The tactic in the first half was to be solid in defence because Holland are stronger," Komazawa said. "We were too defensive though and should have attacked more."
Nicola White opened the scoring for Britain against South Korea before Kim Darae equalized.
Crista Cullen and forward Alex Danson then put the British 3-1 up but South Korea bounced back again with two goals of their own, from Han Hye-lyoung and Park Mi-hyun.
Georgi Twigg and Chloe Rogers scored in the space of a minute to seal the British victory.
Temporary captain Helen Richardson, who has replaced Kate Walsh as she recovers from a broken jaw suffered against Japan, attributed the late comeback to the home support.
"When we conceded a goal to make it 3-3, hearing the crowd roar and really get behind us at that point — there was no doubt we would win the game," she said.
In other matches later Tuesday, first-time Olympians Belgium held Beijing silver-medallist China to a goalless draw to win their first point of the tournament; and New Zealand beat the South African team 4-1 to move into first position in Pool B.
Kiwi captain Kayla Sharland scored two field goals, while defender Clarissa Eshuis and Charlotte Harrison — who celebrates her 23rd birthday today — both scored from penalty corners. The result put New Zealand at the top of Group B, the only team in the pool to win both its matches so far.
In the day's last match, Australia came from a goal down to beat Germany 3-1.
Katharina Otte gave Germany the early lead from a penalty corner and Hope Munro equalized in the 20th minute.
In the second half, Anna Flanagan and Fiona Boyce both converted penalty corners to give Australia the win.
William Haydon contributed to this report.