Morata has struggled in the final third this season, but the Spaniard netted the decisive strike as the Blues edged to victory at Stamford Bridge.
The striker did not always impress in Thursday's fixture in West London, but Cahill was delighted that it was his teammate who made the difference.
Cahill told BT Sport: "We missed a few chances but Alvaro Morata scored the goal to win us the game. I am sure for every striker, scoring goals gives them confidence.
"Morata made some good runs tonight and delighted to see him hit the back of the net. He has scored many goals and were are delighted we won."
The former Real Madrid man has now contributed two goals from eight starts and two substitute outings in all competitions.