The 20-year-old summer signing from Nordsjaelland played for the duration of the game and produced a dominant performance in the middle of the park.
Goals from Dusan Tadic, Morocco's Zakaria Labyad and Lisandro Martinez steered the hosts to victory but Kudus played crucial defensive and attacking roles for Ajax at the Johan Cruyff Arena on Sunday.
He managed the joint-highest number of tackles (5) in Erik ten Hag's team alongside Perr Schurrs and he also completed the highest dribbles (3) with the most pass accuracy (92.2 per cent).
He addition, he registered the second-highest number of shots (4) behind Labyad (5).
After missing a penalty in the 13th minute, the Moroccan forward made amends and found the back of the net just after the half-hour mark.
After the restart, Burkina Faso international Lassina Traore replaced Labyad as Ajax cruised to their second straight win in the Eredivisie. They are second in the Dutch top-flight standings, level on six points with leaders Heerenveen.
Kudus will be looking to maintain his impressive performance when Ten Hag's side host Vitesse for their next league match on Saturday.
The Ghanaian midfielder moved to the Netherlands on a five-year deal in July after his goalscoring exploits for Nordsjaelland in the Danish Super Liga last season, where he scored 11 goals in 25 appearances.