The 26-year-old played 80 minutes as the Eagles recorded a 3-0 win at the Vodafone Arena to go second on the league table.
He was replaced by Oguzhan Ozyakup.
"Great 3 points well deserved," he posted on Twitter after the game.
Besiktas took the lead after 18 minutes through Guven Yalcin in the first half.
Second-half goals from Cyle Larin and Ozyakup, who replace Mensah, sealed the victory for the giants.
Bernard Mensah is currently on loan from super lig rivals Kayserispor but could make a permanent move at the end of the campaign.
He has played 13 games and scored twice for the Turkish giants.
Great 3 points well deserved .. pic.twitter.com/vpWurXI93G— Bernard Mensah (@oliver_mens) December 28, 2020