The US team finished second to Bahamas in the heat in identical times of 2:58.87, the fastest time ever run in the first round of the relay at the Olympics.
The 25-year-old Mitchell had slipped on a stairway in the Olympic Village earlier this week, and that misfortune reared its head after just 100 metres of his one-lap run.
“I got treatment and I was fine. When I warmed up today, I felt really well. I felt I could go 44 (seconds)-low. But as soon as I took the first step past the 200m mark, I felt it break.”
Mitchell added: “I heard it. I even put out a little war cry, but the crowd was so loud you couldn’t hear it. It felt like somebody literally just snapped my leg in half. But I didn’t want to let those three guys down, or the team down, so I just ran on it.”
After the race, Mitchell was x-rayed and team doctor Bob Adams diagnosed it as a break of his left fibula bone.
Rudisha sets 800m WR
Meanwhile, David Rudisha of Kenya won the 800m gold setting a new world record of 1min 40.91secs. Botswana’s Nijel Amos took silver (1:41.73) and Kenyan Timothy Kitum (1:42.53) bronze.