Chances were at a premium in the first 45 but Cesc Fabregas tended to be at the heart of Chelsea's best stuff.
Nevertheless, Chris Hughton's side were resilient at the back and were in no mood to be carved open.
Tiemoue Bakayoko should have done better when he prodded wide after meeting Antonio Rudiger's knockdown, before screwing a shot horribly wide.
Fabregas then put in Victor Moses with a chipped through ball but Matt Ryan made the save to ensure the two sides went in level at the break.
It didn't stay that way for long though, with Morata heading the 'Blues' in front just 45 seconds into the second half.
Cesar Azpilicueta was given space to cross and the former Real Madrid stole to nod past Ryan and open the scoring.
With that, Chelsea were a team transformed and threatened frequently, first Eden Hazard fizzed and effort from 20 yards just wide, before Ryan was called into action to keep out Alonso's 30-yard free kick.
The left-back wasn't denied for too long though as he rose highest at the near post to flick Cesc Fabregas' corner into the back of the net with an hour gone.
Hazard showed his dancing feet as the game went on and only a goal-line clearance from Lewis Dunk prevented him from one of the goals of the day after he had danced past several Brighton players.
In the end though it didn't matter as Chelsea eased to their fourth win in five games to move just a point behind Manchester United in second.
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