They surpassed the previous record of 263-5, set by Royal Challengers Bangalore in 2013
The 35-year-old Swiss is looking to become the oldest man in the professional era to win the title and has not dropped a set in his opening three encounters at this year's tournament.
World number 30, Zverev, who had not beaten Federer in four previous attempts, hoped to upset the 18-time Grand Slam champion by doggedly following his serve into the net, but had only limited success.
He forced a tiebreak in the first set, which Federer won without losing a point on serve, and then the Swiss took control, breaking once in each of the next two sets before wrapping up victory with an ace.