Celtic reeled off a 10th straight win against Aberdeen – a ninth under Brendan Rodgers – to restore their nine-point lead in the Premiership.
Both sides missed chances before Moussa Dembele headed in James Forrest’s cross at the back post for the opener.
Celtic had Mikael Lustig sent off for a second yellow card 15 minutes from time but Kieran Tierney slammed in a second.
The Dons’ frustration boiled over when debutant substitute Sam Cosgrove was sent off for a lunge at Scott Brown.
It left Aberdeen, runners-up for the past three seasons, 12 points adrift of the champions.