Grammatically, you can make those changes and give the sentence a parallel structure. However, if that's what you wanted to do, I would recommend using an Oxford comma before the conjunction and:
The 9.0-magnitude quake triggered a tsunami that devastated northeastern Japan, killed nearly 16,000 people, and caused a nuclear disaster at Tokyo Electric Power's Fukushima Daiichi power plant.
That's the way a similar sentence is punctuated on this website, which explains parallel constructions:
This afternoon, Harry played tennis, returned overdue library books, and ate a mushroom and pineapple pizza.
However, I prefer the original:
The 9.0-magnitude quake triggered a tsunami that devastated northeastern Japan, killing nearly 16,000 people and causing a nuclear disaster at Tokyo Electric Power's Fukushima Daiichi power plant.
That wording suggests that the quake caused the tsunami, and, in turn, the tsunami caused the nuclear disaster and the deaths of 16,000 people. Your suggested revision, however, suggests that the quake was the direct cause of all three calamities – that wording might be more appropriate if, say, many buildings collapsed during the quake, causing most of the deaths.