A fast start from the Gunners soon fizzled out, and City took control of the Wembley showpiece.
The scores remained level at the break, but two quickfire headers from O’Reilly soon after set City up for another Cup success, and sent Pep Guardiola dancing down the touchline.
It is the fourth League Cup final defeat in a row for Arsenal, who will now concentrate on winning the Premier League, Champions League and FA Cup.
More follows.