The former Real Madrid striker gave Chelsea a barely deserved half-time lead from an uninspired first 45 minutes, rifling home after controlling compatriot Pedro’s cross.
Maurizio Sarri’s men weren’t at their best and David Luiz was caught ball watching when Andros Townsend played a quick one-two with James McArthur before firing low past Kepa Arrizalabaga.
Sarri then threw on Hazard, and the Belgian’s first involvement was to be chopped down midway inside the Palace half – before releasing a free-kick through to Morata, who arrowed a shot into the far corner.
Five minutes later Chelsea had breathing room as Morata again did well to leave Marcos Alonso’s cross for the onrushing Pedro to slot home.
Morata had the chance to complete a fine display when put clean through by Hazard in stoppage time, but failed to fool Hennessey with his attempted chip.
At the Etihad, Raheem Sterling scored twice fresh from agreeing a new five-year contract with Manchester City as the champions swept aside Southampton 6-1 to return to the top of the Premier League table.
Sergio Aguero, with his 150th league goal, David Silva and Leroy Sane were also on the mark as Pep Guardiola’s side continued their unbeaten start to their title defence.
Southampton had the minor consolation of becoming the first team in 630 minutes to score against City courtesy of a Danny Ings penalty, but the leaders’ form is ominous for the rest of the division.