The Swede's goal came in the 57th minute and secured a 1-0 victory for Liverpool.
Teammate Cody Gakpo sent the ball into the penalty area and, after a bit of a bounce, it landed in front of the Swede, who scored the only goal of the match with a fine finish.
The goal against Bournemouth was the striker's fourth league goal in five games. He was substituted in the 81st minute.
He took the chance after a quiet afternoon - and that's what a striker's job looks like, Liverpool coach Andoni Iraola said after the match, according to the AFP news agency.
The Spaniard, who left his coaching job at Bournemouth this summer, however, wants more from the 26-year-old.
He had a couple of chances. A cross that he didn't hit cleanly, one when his touch wasn't right and then the goal.
But he has to help us get closer to the penalty area, Iraola continued, also emphasizing that he wants to see Isak more involved when Liverpool has the ball.
Isak joined the big club from Newcastle before last season for a record fee of 125 million pounds (approximately 1.6 billion kronor), but then he only scored three goals in 14 Premier League matches after having large parts of the season ruined by injuries.
The Swedish national team will gather in Stockholm on Monday for four matches in the Nations League in eleven 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.
