Goals from Omar Marmoush, Bernardo Silva and Nico Gonzalez lifted City up into third heading into Sunday’s final round of matches.
Mateo Kovacic’s red card 20 minutes from time could have given Bournemouth hope, but Lewis Cook was also sent off just minutes later for a lunge on Gonzalez.
There was further cause for celebration for City late on when Ballon d’Or winner Rodri made his first appearance since September as a substitute after suffering a serious knee injury.
City’s victory means a point when they travel to Fulham on the final day will be enough to secure a top-five finish thanks to their much superior goal difference compared to sixth-placed Aston Villa.
Just three days on from the disappointment of losing the FA Cup final to Crystal Palace, City had to raise themselves on an emotional night at the Etihad in De Bruyne’s final home match.
Earlier in the day City had unveiled a mosaic and named a road at the club’s training ground after the Belgian.
De Bruyne, who won six Premier League titles and the Champions League during his decade in Manchester, was greeted by a huge banner reading “King Kev” as he led the teams out.
Marmoush saw a penalty saved in City’s defeat at Wembley on Saturday which ensured they will end the season without a major trophy for the first time since Pep Guardiola’s debut season in 2016/17.
Missing out on the Champions League would arguably be an even bigger blow for a club who have not failed to qualify for Europe’s elite competition in 14 years.
Marmoush made amends for his Wembley woe in stunning fashion when he crashed home a long-range effort off the inside of the post on 14 minutes.
The moment an expectant crowd had been waiting for looked set to appear moments later when Marmoush squared to give his captain an open goal.
Yet, De Bruyne could only spoon the ball onto the crossbar from point-blank range much to his own disgust.
That miss could have had more damaging consequences for City had Evanilson found the net rather than hitting the post with a great chance to level for Bournemouth.
Instead, Guardiola’s men doubled their advantage before the break.
Ilkay Gundogan’s clever reverse pass found Silva, who slammed home at the near post to spark jubilant celebrations from an animated Guardiola.
The City boss was furious when a slack pass from Josko Gvardiol played in Evanilson and he was brought down by Kovacic, denying a clear goalscoring opportunity.
The red card hastened De Bruyne’s goodbye as he was replaced by Gonzalez to a standing ovation.
But the numbers were evened up just six minutes later as Cook caught Gonzalez on the shin with his studs.
The cheer for Rodri’s return came close to matching De Bruyne’s departure. The loss of the Spanish midfielder has played a huge part in City’s decline this season.
Gonzalez was bought in January to mitigate Rodri’s absence but has struggled to hold down a place in Guardiola’s side.
The Spaniard curled in his first Premier League goal with a fine finish on 89 minutes before Daniel Jebbison pulled a goal back deep into stoppage time.
Defeat ends Bournemouth’s challenge to qualify for Europe for the first time as they remain down in 11th and now cannot catch eighth-placed Brighton.
Palace shrugged off the hangover after celebrating their first ever major trophy to beat Wolves 4-2 at Selhurst Park.
Eddie Nketiah made the most of a rare chance to start with a double, while cup final hero Eberechi Eze was also among the scorers. (AFP)
