Vintage Nascar Rolling On Tour Winston Cup T-shirt, The NASCAR Winston Cup Series era was the period of the National Association for Stock Car Auto Racing (NASCAR) from 1971-2003. In 1971, NASCAR leased its naming rights to the R.J. Reynolds Tobacco Company who named the series after its premier brand "Winston". The series was referred to as the NASCAR Winston Cup Series from that point forward. Many view the Winston Cup Series Era as a time in which NASCAR entered the modern era of spectator sports. During this era, NASCAR experienced a significant rise in popularity that persisted until Winston left the sport after the 2003 season.