The Turkey international midfielder came on as a second-half substitute in Los Blancos’ 7-1 victory over Osasuna in the Primera Division at the Santiago Bernabeu when he replaced Sami Khedira.
Sahin joined Madrid from Borussia Dortmund during the summer transfer window but had been suffering a knee injury since then.
The 23-year-old was glad to have finally featured in a competitive match for the Spanish giants and thanked everyone at the club for their support.
"It's been a great day for me,” Sahin told Madrid’s official website. “I wish to thank everyone at the Santiago Bernabeu, my team-mates, the manager and the president. I must now work hard to be able to help the team.
"I'm very happy for playing my first game with Real Madrid. It's been difficult being injured.
“I was a little nervous before coming on because it was my first match before the fans. I felt confident and happy after a couple of minutes.”
“We must continue to work hard because we will face difficult games after the league break,” he added.
The victory saw Madrid retain their position at the top of the table in the Spanish first division as they moved to 28 points from 11 matches, three ahead of second-placed and defending champions Barcelona.