Dann, who was Palace's joint-top goalscorer last season, scored his third goal of the campaign in the 4-1 win over Stoke City on Sunday, while Townsend hit his first for the club since his summer move.
"Me and Scott had a friendly bet who would score more goals this season," Townsend said. "Seeing him go 3-0 up, I knew I had to claw it back before it was too late!
"Scott is a fantastic player. He is always up there with the top scoring centre-backs and is doing it again this season. I am sure he will get a few more.
"I want to be in double figures. I have not really set a goal - I think it is too early in the season to set goals. I just want to perform and be effective. Just one more than Scott would be nice. There is no prize between us - just pride. We are two proud players and I think pride is enough."