Manchester City had dominated since kick-off, and it did not take long for more goals to follow Gundogan’s opener.
The impressive Kevin de Bruyne made it 2-0 with a dazzling solo strike, gliding to the corner of the area before bending the ball into the bottom corner with the outside of his boot.
Phil Foden made sure of the points before half-time, running on to a De Bruyne pass and letting fly with a shot that Cherries keeper Mark Travers got his body behind, but could not keep out.
Bournemouth spent most of their time defending in a compact 5-4-1 formation, and only forced home keeper Ederson into action once, through a Ben Pearson snap-shot from the edge of the area.
Jefferson Lerma’s own goal made it 4-0 for City. Lerma was trying to stop Joao Cancelo’s low cross from reaching substitute Bernardo Silva, but only succeeded in sending the ball spinning past Travers to complete an afternoon to forget for his team.