Almost 500,000 people passed through the airport last month, up 5.3% on the same period last year, while Edinburgh Airport had a 1.7% drop in passenger numbers.
Domestic and international traffic grew by 6.1% and 3.9% respectively at Glasgow, giving the airport its busiest November since 2008.
International growth was primarily driven by Emirates's double daily service to Dubai and strong performances from operators KLM and easyJet, the airport said.
Amanda McMillan, airport managing director, said: "To have enjoyed our busiest November in four years and to see both domestic and inter-national services performing well is very encouraging.
"We have been buoyed by some very positive recent announcements and remain committed to further strengthening Glasgow's connectivity by growing our route network."
Passenger numbers at Aberdeen Airport also increased last month. It handled more than 272,000 passengers in November, up 4.8% on last year.
Since the start of the year Aberdeen has recorded an annual increase of 8.7%, with around three million people using the airport between January and November.
Edinburgh Airport, taken over by Global Infrastructure Partners earlier this year, said passenger numbers were down 1.7% last month, although domestic traffic increased 1.9%, the first monthly rise since June.
A 6.8% fall in international traffic was attributed to cuts in the winter schedule of budget airline Ryanair, amid a row over landing charges which has now been resolved.
Overall, 631,321 passengers used Edinburgh Airport – Scotland's busiest – in November.
Ryanair announced last week it is to add six new destinations from Edinburgh Airport.
Gordon Dewar, chief executive of Edinburgh Airport, said: "Clearly, I'm happy to see our domestic performance come back into growth but this is tempered with disappointment at the temporary decline in international traffic.
"We always knew Ryanair's cuts would bite and they have. That is why last week's deal was a key priority for my team and I. Ryanair is one of our biggest customers and to fall out with a large customer is never good.
"I'm glad we could work with them to gain trust and understanding to ultimately create a foundation on which we can together deliver more routes for Scotland."