what was the make of the car that won the first gp won on goodyear tires?...?

Answer 1

A Honda RA272, driven by Richie Ginther of the U.S. recorded the first Formula One Grand Prix win for Goodyear on October 24, 1965 at the Mexican Grand Prix. .
It was also the first and only win for Ginther, who started the race from the third position on the grid.
The second win for a Goodyear-shod car came a year later when Australian Jack Brabham won the 1966 French Grand Prix on July 3 at Reims; he was driving a Brabham-Repco.
Interestingly, Ginther's car carried No. 11 and Brabham's No.12.

Answer 2

According to my info, the first Formula 1 Grand Prix win with Goodyear tires was in 1965 at the Mexican Gran Prix. Richie Ginther drove car #11 which was a Honda RA272.