Edinburgh saw 794,792 passengers for the month, a year-on-year increase of 12.4%, and its 'busiest November ever'.
Glasgow's monthly figure of 618,583 was a rise of 7.7% on November 2014.
The figures suggest Edinburgh Airport will have its busiest year on record in 2015, while Glasgow Airport will be busier than in any year since 2008.
International traffic has been especially strong at Edinburgh, with annual growth of 22.5%.
Qatar Airways has expanded its service to Doha, and numbers are reported to be up on routes operated by easyJet, Ryanair, Etihad and Turkish Airlines.
Edinburgh Airport Chief Executive Gordon Dewar said: "These exceptionally strong figures represent our busiest-ever November; Edinburgh Airport has experienced passenger numbers levels in November - a quiet month in air travel - on a par with what many other regional airports do at the peak of summer.
"This tremendous achievement is a direct result of our commitment to increasing connectivity and choice and improving the passenger experience.
"This has been another record-breaking month and is a sure sign of the growing success of both Scotland and Edinburgh as a destination which emphasises our position as a key driver for Scotland's economic growth."
Glasgow's international traffic was up 12.2%, with new services to Budapest, Vilnius, Lublin and Berlin.
Domestic services have also expanded, with a new route to Exeter and extra capacity on flights to Gatwick and Stansted.
Glasgow's managing director Amanda McMillan said: "2015 has been a fantastic year in terms of passenger growth. Our November figures not only guarantee we will end the year on a high, they will ensure we are in a strong position as we prepare to enter 2016, the airport's 50th anniversary year.
"In addition to gearing up for the Christmas getaway, we have already seen a new service to Milan launch this month with easyJet and there is more to come before the end of the year.
"Later this month Blue Air and Wizz Air will both begin a new service to the Romanian capital of Bucharest and British Airways will start a new Saturday service to Salzburg for the ski season."

The Project Literacy alliance says that 11% of the world's population remains unable to read or write.
The campaign is lobbying leaders attending the United Nations general assembly in New York, which has been setting global education targets.
"The curse of illiteracy is global and devastating," said campaign spokeswoman Kate James.
The Project Literacy campaign says it is creating a virtual "petition" on behalf of 757 million people who cannot write their own name.
The partnership brings together charities such as the National Literacy Trust, BookAid and Room to Read, along with education businesses such as Pearson.
The campaign says that illiteracy is a major barrier to economic development, costing $1.19 trillion (Â£1.25tn) per year.
Global education targets, such as the goal of providing primary education for all, have been set since 1990.
But the campaign says that in sub-Saharan Africa, there are 37% more illiterate adults than there were in 1990.
The project highlights the gender gap in who is taught to read and write. Women represent about five in seven of those who are illiterate around the world.
The campaign argues that literacy is linked to better health, reducing crime, job opportunities and democratic engagement.
There are 32 million illiterate adults in the United States and more than 70% of the US prison population have the literacy levels of a nine-year-old or lower.
The impact of illiteracy was "inequality, poverty and disease", said Ms James.
World leaders have been gathering at the United Nations to approve global development targets - the sustainable development goals.
These replace pledges made in the millennium year.
Although some progress was made, none of the targets for education, such as universal primary education, were fully achieved by the deadline of 2015.
Passenger numbers grew significantly in November at Scottish airports, with the introduction of new international services.
[NEXT_CONCEPT]
A coalition of charities and businesses is calling on world leaders to make tackling illiteracy a global priority.