After a long day of qualifying involving every female gymnast who came to London, the Americans had the top team score and three of the four best individual totals.
Raisman, Gabby Douglas and Wieber paced the United States to a qualifying score of 181.863 points. Russia was second with 180.429 and China third at 176.637. Those points will not carry over when the team gold medal is decided.
The qualifying determines which eight countries will battle for the team title on Tuesday, which 24 gymnasts will compete for the all-around gold medal and which eight competitors will take part in the finals for the four separate disciplines that make up the sport.
The rules state, however, that no more than two athletes from any one country can be in any of the individual finals.
Wieber won the world title in Tokyo last year and she finished fourth in qualifying on Sunday. But because Raisman and Douglas were second and third, Wieber will not be allowed to take part in the all-around final.
"It is a bit of a disappointment," Wieber said. "It has always been a dream of mine to compete in the all-around final of the Olympics. But I'm proud of Aly and Gabby and happy that they reached the all-around and that I was able to help the team get to the [team] finals."
The Americans also won the team gold medal at the world championships last year.
Victoria Komova of Russia had the individual qualifying lead going into the late-night session with 60.632 points. Raisman totaled 60.391, Douglas had 60.265 and Wieber 60.032.
Wieber's chances to make the all-around final were damaged by a flawed routine on the beam. She scored a 14.700 on that apparatus while Douglas had a 15.266 and Raisman a 15.100.
The United States, Russia and China will be joined in the team final on Tuesday by Romania, Britain, Japan, Italy and Canada.
The men's gymnastics squad from the United States also led qualifying on Saturday and will try for a gold medal in the team event on Monday.
Toddler uninjured after being knocked over by Obama family dog
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'