Morata was unavailable for the goalless draw at Everton three days previously but his firepower inspired the champions following a lifeless first half that saw a number of fine chances wasted.
It was a familiar sight that broke the deadlock as the Spain striker combined with international teammate Cesar Azpilicueta, nodding home the full-back's pinpoint cross a mere 40 seconds after the interval.
The Spanish theme to the victory continued when Marcos Alonso headed in Cesc Fabregas' corner for the second, sweeping the match beyond the reach of the outclassed visitors.
Brighton had not won in the fixture since an FA Cup triumph in 1933 and that record was never under threat as Eden Hazard expertly pulled the strings to cement third place for Antonio Conte's men.
It took 18 minutes for Chelsea to create their first chance when Fabregas, recalled following the 0-0 draw at Goodison Park, whipped the ball to beyond the far post where Antonio Rudiger jumped high to nod the cross down to Tiemoue Bakayoko.
Bakayoko was stood four yards out from goal yet managed to shoot wide from a great position, his only mitigation being the speed of Rudiger's header.
The pressure on the Brighton goal was increasing steadily and Victor Moses was the next to fluff his lines by directing the ball straight at goalkeeper Mat Ryan from point blank range.
Moses was drifting into dangerous positions around the right post but if the final pass was accurate then his first touch or finishing was found wanting.
Fabregas and Rudiger each pulled the trigger just outside of the area but neither shot troubled Ryan, who then positioned his body behind a strong attempt by Hazard despite the acute angle.
The second half had barely begun when Chelsea broke the deadlock, Azpilicueta and Morata linking up for the striker to nod home his 12th goal of the season.
Azpilicueta forced a brilliant save from Ryan as his free-kick powered towards the top right corner, but there was nothing the keeper could do to stop the champions' second in the 61st minute.
Fabregas curled in a corner that was met by Alonso with a glancing header and with no one defending the far post, the ball careered into the net.
Having weaved Brighton's defence into a knot, Hazard saw a shot cleared off the line by Lewis Dunk before the Belgian playmaker teed-up Bakayoko, whose accuracy was poor once more.
Chelsea stepped off the gas for the remainder knowing the job was done.