The 33-year-old came on as a second-half substitute for Daniel James in the 58th minute, and with his first touch, diverted an effort from Bruno Fernandes’ cross just past Edouard Mendy’s near post.
Cavani also showed off his excellent movement which has made him one of Europe’s most feared No.9s over the past decade.
The veteran forward left Paris Saint-Germain in June with an astonishing record of 200 goals in 301 appearances, making him the French club’s all-time top goalscorer.
United had the better of the chances at Old Trafford, with Chelsea needing three good saves from their goalkeeper Mendy to keep the score level.
Former Red Devils left-back Evra highlighted Cavani’s performance as one of the positives from the drab draw at Old Trafford, and believes his big character is a perfect fit for Ole Gunnar Solskjaer’s side.
‘I was so happy with this signing,’ Evra told Sky Sports after the game at Old Trafford.
‘Look at this first chance, first touch at the near post. This is a striker. This is what we want. If you ask any real PSG fan who is their favourite player they will say Cavani. They won’t say [Kylian] Mbappe or Neymar they will say Cavani.
‘I am really pleased, I know people were expecting a Sancho. But United need character.
‘We will see about his fitness but I wish him well and what a good signing for Man Utd.’