"You came face to face with Godzilla," Verstappen's engineer told him on the radio as the reptile sauntered to safety.
Germany's Nico Rosberg edged out the young Dutch driver at the top of the timesheets, with Mercedes team mate and championship leader Lewis Hamilton still struggling ahead of qualifying.
Rosberg, two points behind Hamilton, lapped the 23-turn Marina Bay Street Circuit in one minute 44.352 seconds, just 0.059 ahead of 18-year-old Verstappen, suggesting the race for pole will be a close-run affair.
Ferrari's Kimi Raikkonen was third fastest, half a second down on Rosberg, with Red Bull's Daniel Ricciardo and the other Ferrari of Sebastian Vettel close behind.
Hamilton has seen his 19-point lead at the top of the standings dwindle away in the last two races and his inability to get the best out of the fastest ultrasoft tyres left him down in eighth place, his 1:45.806 time set on supersofts.
The hour-long session got off to an eventful start with Manor's Pascal Wehrlein losing most of his rear wing after spinning into a wall, bringing out a red flag as marshals scampered to clear the debris.
The Monitor lizard's appearance, as cars were heading back to the pits, shocked Verstappen.
Practise resumed with Sauber's Felipe Nasr spinning at the Turn 13 hairpin after almost hitting Esteban Gutierrez's Haas.
The Mercedes pair were first to emerge for qualifying simulations and Rosberg quickly set a new fastest lap while Hamilton locked up and ran through turn seven into the exit road for the second time in 15 minutes.
The Briton aborted one final attempt to set a fast time and his lack of a long-run race simulation due to a hydraulics problem on Friday will also be a major concern for both the driver and his team.
(Editing by Alan Baldwin and Ian Chadband)
