Hamilton's Mercedes team topped both practice sessions in the desert on Friday, but Verstappen led the way in the final running before qualifying.
Verstappen finished just 0.074 seconds clear of Hamilton at the Yas Marina Circuit to suggest a close battle in the shootout for pole position later on Saturday.
Valtteri Bottas was quickest on Friday, but he will start the race from the back of the field following an engine change.
The Finn, who finished third on Saturday, was forced to take on a new power unit after he retired with an oil leak at the last round in Brazil.
Overnight, his Mercedes team then discovered a pneumatic failure in his fresh engine, which required a host of replacement parts.
The four-time world champion finished 0.409 sec adrift of Verstappen. Charles Leclerc was fractionally further back in sixth.