The 28-year-old, who joined the Potters from Schalke 04 this summer, opened scoring with two minutes left in the first half and later rescued a point for the Bet365 Stadium outfit.
Choupo-Moting expressed his delight after opening his English topflight goalscoring account against Jose Mourinho's men.
"We came back after 2-1 down so personally I'm happy for my goals but most importantly we played a great game at home,” Choupo-Moting told BTSport.
"My aim is always to score or get an assist so I'm very happy we didn't lose and I'm happy for my first goals for Stoke - I hope to continue like that.
"A striker is always rated by assists and goals but I always try to play well and give 100% for the team.
"Games like against Arsenal we did great - I didn't score but I felt I did a good performance.
"I hope there are more goals coming. We've had two strong teams at home - Arsenal and Manchester United - and we did well both times,' he concluded.