The best way to fight Inflation is to reduce Maintenance, use the cheapest civics (although some of the medium and high costing ones can pay for themselves with their bonuses), and use less units (or civics that give free units).
In my Bannor Order game I had -120% Maintenance in most of my cities so I only paid Maintenance for the newly captured cities and some that hadn't finished the courthouses and that order building. I had a large territory and 8 law mana (-40% from just them)
EDIT:
And a big empire that can handle its Maintenance costs are usually better shaped at handling the inflation since they got more income (usually).
And Merchant focus helps. Having a city with multiple Great Merchants settled, with 6 or so Merchants and the Bazaar of Mammon helps a lot, especially with a holy city. And having RoK temples in most cities help too.