Hamilton's lap time of One minute 20.914 seconds was only four tenths of a second slower than last year's fastest race lap, highlighting the increased grip that was expected this year, with the 2015 race taking place not long after the track was re-laid.
Sebastian Vettel was second, less than a tenth of a second behind Hamilton, with Kimi Raikkonen a little further behind, 0.158 seconds behind the pacesetting Mercedes.
Verstappen had to miss the second half of the session after a break fire caused damage to his wiring loom, although the damage will be fixed before second practice.
The second Mexican in the field, Esteban Gutierrez, was 15th, ahead of Fernando Alonso and Felipe Nasr - who caused the session's only red falg after his front wing failed spectacularly following a trip over the high curbs.
Bahrain International Circuit - Winter testing