Starting from a record 88th pole position, the 34-year-old Briton was unchallenged from lights to flag as he cruised to an untroubled triumph 16 seconds ahead of Red Bull’s Max Verstappen and Charles Leclerc of Ferrari, who faced a post-race investigation for fuel irregularities.
The six-times world champion’s success extended his points-scoring run to a record-equalling 33 races, levelling with his own record, and brought him his 50th victory from pole position.
His fifth win at the Yas Marina circuit also drew level with Ayrton Senna in claiming a 19th start-to-finish triumph.
Hamilton’s Mercedes team-mate Valtteri Bottas, who had started from the back of the grid after taking a new engine, came home fourth ahead of four-time champion Sebastian Vettel in the second Ferrari and Alex Albon in the second Red Bull.
It was a welcome morale boost for the competitive Finn, three days after announcing the end of his three-year marriage to Emilia.
Sergio Perez took seventh for Racing Point on the final lap, Lando Norris was eighth for McLaren, Daniil Kvyat of Toro Rosso ninth and Carlos Sainz, in the second McLaren, took 10th.
“That was an absolute master-class,” Hamilton’s race engineer Peter Bonnington told him on team radio. “You didn’t even break into a sweat!”
The winner, who secured title number six with two races to go in Texas last month replied: “I can assure you, I am definitely sweating.”
Hamilton scored a classic ‘grand slam’ with pole position, fastest lap and race victory.