Like-for-like sales were up by 4.9% during the quarter compared with a year earlier, in part due to the continued success of meal deals.
The company said it would continue to benefit from "low cost pressures and a stronger consumer environment".
But it warned that wage pressures could drive costs up next year.
Chief executive Roger Whiteside told the BBC that the chain already paid staff more than the national minimum wage, but that rising labour costs would lead to "longer term inflationary pressure".
He said the business would "look for cost efficiencies to offset" any rising costs, but added that labour costs "held no fear for us".
Shares in Greggs opened sharply higher and continued to climb in afternoon trading.
"The good times continue to roll for Greggs, with the bakery chain posting an impressive third quarter performance, following on from a dynamic 51.3% increase in first half pre-tax profits," said George Scott at retail analyst Conlumino.
The chain said meal deals, where customers can buy a drink together with food at a discount, were proving popular, particularly at breakfast time.
Greggs has refitted 158 stores this year, while opening 65 and closing 47. The company now has 1,668 outlets.
"We have the High Street pretty well covered," Mr Whiteside said, so most new openings would be in other areas, such as motorway services and garage forecourts.
Shares in Greggs have jumped more than 10% after the bakery chain reported stronger than expected sales for the July-to-September period.