Early in the session, Hamilton was on the quicker ultrasoft tire compound when the rear of his car spun, but he regained control.
In hot and dry conditions on the Yas Marina circuit, Hamilton was 0.374 seconds quicker than Formula One rival Nico Rosberg, and 0.428 better than Dutch teen Max Verstappen.
Verstappen's Red Bull team-mate Daniel Ricciardo was fourth, followed by Ferrari's Sebastian Vettel, who won the first of his four straight F1 titles here in 2010 when he was driving for Red Bull.
That dramatic championship went to the last race and so is this one.
Hamilton is bidding to win the title for the third straight time and fourth overall, but the odds are in Rosberg's favor.
The German driver leads the championship by 12 points and can afford to finish third even if Hamilton wins on Sunday.
There is a second practice in the evening, when track temperatures will be similar to those expected for the race.
In what is expected to be his final GP, British driver Jenson Button drove with a bright yellow helmet similar to the one he wore during his F1 title-winning campaign with Brawn in 2009.
Although Button has an option with McLaren for the 2018 season, he said on Thursday he does not expect to race again. Brazilian Felipe Massa, who drives for Williams, is categorically retiring after this race.
Both started their F1 careers at age 20.
Meanwhile, French driver Romain Grosjean's frustrating recent form continued as he came back to the garage before the end because of a braking issue on his Haas car.
Abu Dhabi - First free practice:
1. Lewis Hamilton (Britain) Mercedes 1:42.869
2. Nico Rosberg (Germany) Mercedes 1:43.243
3. Max Verstappen (Netherlands) Red Bull - TAG Heuer 1:43.297
4. Daniel Ricciardo (Australia) Red Bull - TAG Heuer 1:43.362
5. Sebastian Vettel (Germany) Ferrari 1:44.005
6. Sergio Perez (Mexico) Force India - Mercedes 1:44.155
7. Kimi Raikkonen (Finland) Ferrari 1:44.556
8. Carlos Sainz Jr (Spain) Toro Rosso - Ferrari 1:44.685
9. Felipe Massa (Brazil) Williams-Mercedes 1:45.039
10. Marcus Ericsson (Sweden) Sauber - Ferrari 1:45.168
11. Alfonso Celis (Mexico) Force India - Mercedes 1:45.476
12. Romain Grosjean (France) Haas - Ferrari 1:45.600
13. Felipe Nasr (Brazil) Sauber - Ferrari 1:45.778
14. Esteban Gutierrez (Mexico) Haas - Ferrari 1:45.925
15. Valtteri Bottas (Finland) Williams-Mercedes 1:45.940
16. Jolyon Palmer (Britain) Renault 1:46.219
17. Kevin Magnussen (Denmark) Renault 1:46.372
18. Fernando Alonso (Spain) McLaren 1:46.379
19. Pascal Wehrlein (Germany) Manor - Mercedes 1:46.458
20. Jenson Button (Britain) McLaren 1:47.127
21. Jordan King (Britain) Manor - Mercedes 1:47.558
22. Daniil Kvyat (Russia) Toro Rosso - Ferrari 2:01.989
Original source: Hamilton ahead of Rosberg in first practice