Edinburgh had its fourth busiest month ever, with passenger numbers up 11 per cent on a year ago to 1,191,728.
Glasgow's increased by 4.2 per cent to 934,295.
The capital's airport growth included international flight traffic up by more than one fifth.
Its annual total was up by nearly 11 per cent to almost 12.1 million.
Chief executive Gordon Dewar said: “These latest set of passenger figures are very welcome indeed and are testament to both the tremendous international draw of Edinburgh and Scotland as a destination and of the hard work we are doing here to attract new airlines and routes.
“We have strong indications that Edinburgh Airport – unlike the majority of the UK airport market – has a healthy balance of inbound and outbound passengers.
“This gives us confidence that we can continue to perform well and help deliver connectivity which creates jobs and delivers growth for Scotland – in spite of any wider economic uncertainty in the sector and economy at large.”
However, Mr Dewar said there was “absolutely no room for complacency” and he repeated his call for Scottish Government to press ahead with its plan to cut air passenger duty.
He said halving the tax would encourage airlines to bring more aircraft to Scotland, which would boost tourism, create jobs and stimulate the economy.
Glasgow Airport chiefs said the Davis Cup and Celtic's Champions League games had helped swell numbers.
They also highlighted Ryanair’s Derry route and easyJet’s Bristol and Belfast services, where extra seats have been added, as contributing to the growth.
There was also a 12 per cent hike in flights to EU countries, including to Brussels, Paris, Milan and Barcelona.
The expansion is expected to continue, with Ryanair launching routes to Alicante, Malaga, Gran Canaria and Lanzarote this month, and Thomson to Cape Verde.
The annual passenger total has increased by nearly 8.2 per cent to 9.2 million.
Managing director Amanda McMillan said: “Our strong performance throughout the year continued in September, which was also the fourth consecutive month the airport carried more than 900,000 passengers.
“We are on course to record our most successful year and this success can be attributed to our continued focus on not only attracting new services, but working closely with our current airlines to enhance existing services."