Hamilton, chasing an unprecedented eighth world title, goes into Sunday's season-closing race level on points with Max Verstappen.
And it was the Dutch title contender who was quickest out of the blocks at the Yas Marina circuit, taking the honours in the morning session.
Hamilton, placed third, turned the tables under floodlights in second practice with a 1min 23.691 lap to get his weekend off to an encouraging start.
"It doesn't feel too bad," said the 36-year-old Briton.
"It started off good but got a bit worse in P1, then started off better in the second session with some changes we made.
"Now we just have to crank through the data and try to figure out how we can improve, where we home in. The target is always moving, but yes. Otherwise, I feel good."
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