Shares of the Louisville, Ky., company at last check rose 7.8% at $82.01.
Papa John's said same-store sales across North America rose 23.8%.
The company reported earnings of $15.7 million, or 35 cents a share, swinging from a loss of $385,000, or 10 cents a share, in the year-earlier period.
Revenue for the quarter rose 17% to $472.9 million from $403.7 million.
A survey of analysts by FactSet for Papa John's produced consensus estimates of GAAP earnings of 35 cents a share, or an adjusted 33 cents, on revenue of $466.1 million.
Papa John's' "strategy and execution [have] helped us outperform our competition and deliver five straight quarters of same-store sales growth," President and Chief Executive Rob Lynch said in a statement.
On Nov. 4, the board approved a buyback program for up to $75 million, or 3%, of the stock, effective through Dec. 31.
In September Papa John's said it would open a new headquarters in Atlanta. The company said it expected to complete the move and related organizational changes by the summer.
The company has offered separation packages to employees who don't relocate to Atlanta.
Papa John's thus expects to incur one-time reorganization costs of $15 million to $20 million for severance and transition, recruitment and relocation and other third-party costs through 2021.
Of that amount, it expects to report $4 million to $5 million for fourth-quarter 2020. The third quarter reflected no "significant corporate reorganization costs," the company said.