Cloverfield (2008) on Netflix

The US Defense Department finds a videotape in the former Central Park. The footage shows a group of friends celebrating a surprise farewell party in the apartment of Rob Hawkins in Lower Manhattan. Rob is a young man that is leaving New York to work in Japan and his friend Hud is recording messages from his friends. Out of the blue, they are surprised by an earthquake and they see on the news that a ship has capsized in the harbor area. They go to the penthouse to see the accident and they actually witness explosions everywhere; when power goes out in the building, they run to the streets trying to save their lives from the attack of the monster.