The Japan Air Lines jet filled with smoke after arriving at Boston, following a non-stop flight from Tokyo.
The fire chief at Logan airport said a a fault occurred in the battery pack for the plane's auxiliary power unit, which runs the jet's electrical systems when it is not getting power from its engines.
Fire crews using infrared equipment found flames in a small compartment in the plane's belly and had the fire out in about 20 minutes, he said.
Massachusetts Port Authority's fire chief Bob Donahue said there was a flare-up later when a rechargeable battery exploded.
He said it was too soon to know the cause.
About 15 minutes after all 173 passengers and 11 crew members had disembarked, a mechanic spotted light smoke in the cockpit and cabin.
"When we arrived, it was a heavy smoke, and that was in three minutes, so this was advancing," Mr Donahue said.
The model was originally planned for launch in 2009 but production has been beset with technical problems. It was first delivered in late 2011.
In November 2010, a test flight had to make an emergency landing after an in-flight electrical fire - delaying test flights for several weeks.
Last month, a United Airlines 787 flying from Texas to New Jersey diverted to New Orleans because of an electrical problem with a power distribution panel.
The head of Qatar Airways recently criticised Boeing after its delivery-delayed planes were grounded for five days because of the electrical faults.
It came as the US aviation watchdog discovered fuel line assembly errors.
It said that the faults could result in fire risk from leaks dripping on hot engine parts or causing the aircraft to run out of fuel.
British Airways has ordered 24 Dreamliners from Boeing and is still expecting its first 787 in May, with a further three due for delivery before the end of 2013.
Virgin Atlantic has 16 Dreamliners on order and told Sky News it still expects its first delivery in 2014.
Thomson Airways has also placed orders for the hi-tech long-haul Boeing plane, which has been marketed as being more comfortable and environmentally friendly than other aircraft.
A spokeswoman for Thomson told Sky News: "Our first Thomson Dreamliner is still on track to be delivered early this year. Boeing has reassured us that they are taking action to rectify the issues highlighted to them."
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