Hamilton led from pole position and dominated throughout for his fourth race victory at the Marina Bay circuit.
The top three remained unchanged from qualifying as Ferrari's Vettel failed to get past the Red Bull of Verstappen.
'Mercedes had no grounds for complaint' - Horner
Hamilton's seventh win of the 2018 season gives him a 40-point advantage over Vettel with six races remaining.
“Great job everyone – what a weekend,” Hamilton says. “Keep pushing. Keep pushing.”
The Brit is favourite to beat Vettel to a fifth world title, level with Juan Manuel Fangio.
Verstappen: 'I don't feel sorry for Hamilton'
Abu Dhabi Grand Prix
'No assurances' Hamilton will race next season, says Mercedes boss Wolff