The United States scored 179.411 points and beat Russia, the defending champion, by 4 points. The Americans did not miss a single routine in qualifying or the team finals, and counted just one score below 14.5 on Tuesday night.

It was the first world title for the United States women since 2007.

China, the Olympic champion, was a distant third. Romania, a traditional power, was fourth.

Losing Sacramone to a torn Achilles last Thursday seemed like a huge blow. Sacramone is the team leader, and she puts up huge scores on the vault, where she’s the defending world champion; balance beam; and floor exercise.

But instead of collapsing, the Americans became stronger, immediately throwing down a challenge to the Russians with three huge scores on the vault.

The teams moved to uneven bars, and Russia pared the American lead to about 1.5 points, but came no closer.