The goal came in the 57th minute and secured Liverpool's 1-0 victory.
Teammate Cody Gakpo sent the ball into the penalty area and, after a little luck with the bounce, it fell to the Swede, who finished superbly for the only goal of the match.
Isak celebrated the goal with the visiting Liverpool fans, which led to a warning.
Isak joined the big club from Newcastle ahead of last season, but managed only three goals in 14 Premier League matches after the 26-year-old had large parts of the season ruined by injuries.
The goal against Bournemouth was the striker's fourth league goal in five games. He was substituted in the 81st minute.
The Swedish national team will gather in Stockholm on Monday for four matches in the Nations League in 11 days.
The Blue and Yellows face Romania on Friday and Poland three days later at the national arena in Solna. After that, away matches against Bosnia-Herzegovina and Romania await.
