Flight 1168, a Boeing 737-900, was carrying 174 passengers and six crew members when engine trouble began as the plane neared George Bush Intercontinental Airport.
One passenger told Houston media outlets that he heard a loud bang, felt a strong vibration and saw a flash of light.
"I noticed as we were coming into Houston airport, I heard sounds that I don't normally hear when I fly," passenger Leonard Weiner said.
Weiner said the captain came onto the plane and told everyone to evacuate.
Chris Morrison said he was dozing off when he suddenly heard a loud bang that woke him up. He said he saw a flash of light out of the window.
"People were starting to panic," he said. "Everyone kept hitting the flight attendant call button."
Another passenger said he saw flames coming from the engine, but a Federal Aviation Administration spokeswoman says emergency responders found no evidence of fire or smoke.
The passengers jumped out of the plane on emergency slides, and they stayed on the tarmac about a half hour before they were sent to the United Club.
United spokeswoman Rachael Rivas said some people suffered minor injuries while evacuating the plane.
United Airlines released a statement to Eyewitness News about the incident:
"United flight 1168 from Newark, New Jersey, to Houston experienced an issue with one of the engines shortly before landing. After landing safely, customers were evacuated from the aircraft and were bused to the terminal. Local authorities responded immediately and our maintenance team is currently inspecting the aircraft."
FAA spokesman Lynn Lunsford said crews were taking a closer look at the plane Monday.
The emergency came the same day an Ethiopian Airlines' Boeing 737 Max 8 crashed, killing 157 people. Another plane of the same model crashed last October in Indonesia, killing 189. The 737 Max 8 is a newer model that's part of a fleet meant to replace the 737-900 and other Boeing aircraft.
(The Associated Press contributed to this report)
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