The Slovenian substitute's strike salvaged a point at West Ham United last time out, and he was once again the headline-maker, sliding home after 71 minutes to settle a tight contest at Everton's new home.
Sesko ran on to Bryan Mbeumo's pass and slid a shot under Jordan Pickford, a quarter of an hour after being introduced by Carrick.
Senne Lammens was a key contributor at the other end, and the Blues huffed and puffed but failed to make a dent in the Reds rearguard, as we kept a first away clean sheet of the season.
FIRST HALF – INITIAL EXCITEMENT PETERS OUT
The Everton supporters welcomed their side out with a huge flag display and the intense atmosphere generated in the stands transmitted on to the pitch right away.