SYDNEY — As flames spread up the hill toward million-dollar homes, the firefighters scrambled to keep pace.

“It’s starting to move up the trees!” shouted Jason King as Steve Zieba raced ahead with a hose, slipping on the steep incline before aiming his nozzle at a burning eucalyptus trunk. On the cliffside above them, another crew hauled a water line up sheer rocks and through heavy smoke to replace a hose melted by the blaze.

Even as they battled the flames, the firefighters also fed them, using metal canisters called drip torches to ignite the undergrowth. Two helicopters hovered overhead: one dropping water, the other, incendiary pellets.