The incident at Lake Moondarra, near Mount Isa, was captured on camera by local residents on Sunday.
The 10-ft snake, thought to be a python, coiled itself around the crocodile and the two struggled in the water.
The snake later brought the dead crocodile onto land and ate it.
Tiffany Corlis, a local author, saw the fight and took these pictures, which have been widely used in the Australian media.
"It was amazing," she told the BBC. "We saw the snake fighting with the crocodile - it would roll the crocodile around to get a better grip, and coil its body around the crocodile's legs to hold it tight."
"The fight began in the water - the crocodile was trying to hold its head out of the water at one time, and the snake was constricting it."
"After the crocodile had died, the snake uncoiled itself, came around to the front, and started to eat the crocodile, face-first," she added.
Corlis said it appeared to take the snake around 15 minutes to eat the crocodile.
The snake was "definitely very full," when it finished, she said. "I don't know where it went after that - we all left, thinking we didn't want to stick around!"
Another witness, Alyce Rosenthal, told local media that the two creatures fought for about five hours. By the end, they appeared exhausted, she said.
"It's not something that you see every day," she said.
Pythons kill their prey by tightening their coils around the animal as it breathes out.
This can cause the animal to suffocate or suffer heart failure, allowing the python to swallow its prey whole. Many snakes have flexible jaws that enable them to swallow prey many times their own body size.
A 2012 study published in the Royal Society journal Biology Letters suggested that snakes could sense their victim's heartbeat, and let go when it stopped, preventing it from using more energy than required.
The Australian state of Queensland is home to some of the world's most dangerous snakes, as well as saltwater crocodiles.
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