The Ukranian ended his long goal drought after just 11 minutes of the game, making the most of his first start for his new side by converting Marko Arnautovic's low centre.
That clearly boosted the forward's confidence, with his second of the game being vintage Yarmolenko.
The powerful winger picked up the ball out on the right and cut inside two Everton players before curling beyond Jordan Pickford and into the top corner to put daylight between the two sides.
Despite the quality of the finish Pickford was by no means blameless, with his poor pass in the build-up presenting the ball to the visitors.
Credit must be given to Yarmolenko, though, who made the finish look easy despite not having scored since December 2017 going into the match.