The Toffees kicked off their 2017-18 Premier League campaign with a 1-0 victory over Stoke at Goodison Park on Saturday afternoon.
Wayne Rooney, who returned to the Merseyside outfit in the summer transfer window after leaving Manchester United, scored the only goal of the match at Goodison Park in first-half injury time.
Klaassen started the game for Everton and played for 60 minutes, and the 24-year-old attacking midfielder has taken to Twitter to express his delight at the win.
The Netherlands international joined the Premier League club from Dutch giants Ajax in the summer transfer window for a fee reported by BBC Sport to be worth £23.6 million.
A number of other Everton players, as well as manager Ronald Koeman, have also taken to Twitter to revel in the win against Stoke.
Happy to start my premier league adventure with a win pic.twitter.com/APD4ugKnhX— Davy Klaassen (@DavyKlaassen) August 13, 2017
Over the course of the 90 minutes at Goodison Park on Saturday afternoon, hosts Everton had 62% of the possession, took nine shots of which four were on target, and earned six corners, according to BBC Sport.