The British number three needed to go the distance for the fourth successive match before coming through by a 6-2 3-6 6-3 scoreline.
Before he took to court, Evans had watched on as Johanna Konta won the women's event, and the Birmingham-based player seemed inspired by his compatriot's success as he powered through the opening set in 30 minutes.
Kuznetsov - who had prevailed in their only previous meeting at Wimbledon in 2014 - hit back during the second to force Evans into another final-set decider and it appeared that the Russian had the momentum.
However, Evans produced an excellent third set, breaking once and dropping just eight points behind his serve to see out the biggest win of his career.
The 26-year-old will now head into the final against Gilles Muller with the chance to win his first top-tier trophy and break into the world's top 50 for the first time.