City, currently sitting 3rd in the Premier League, are now two points clear of Newcastle, Chelsea, and Aston Villa with just one game remaining.
The win edges them closer to a coveted top-five finish. For Bournemouth, however, their pursuit of 8th place is over.
The evening began in style as Omar Marmoush opened the scoring with a stunning strike in the 14th minute.
Bernardo Silva doubled City's lead before half-time, while Nico Gonzalez added a third just before the final whistle, moments after winning a red-card challenge.
Bournemouth grabbed a late consolation through Daniel Jebbison in stoppage time.
All eyes were on De Bruyne, the talismanic midfielder, who was the centre of attention throughout the match. He nearly marked his farewell with a goal, but struck the crossbar from close range and later missed a clear chance he described as "terrible."
Rodri made a welcome return to the squad after eight months out with injury, featuring for the first time since September.
The game saw tempers flare, with both Mateo Kovacic and Lewis Cook receiving red cards. Kovacic was dismissed for hauling down Evanilson, while Cook was sent off following a reckless challenge on Gonzalez.
"The most important thing was to win the game and we did it against an incredible opponent," said Guardiola.
"They destroyed us in the Premier League in the first leg. The games are always good, we had chances, they had chances, it was open and the people enjoy."
Speaking to the press on the pitch after the game, alongside his family, De Bruyne remarked: "Manchester is home, Manchester is where these little kids are born.
"I came here with my wife to stay for a long time, I didn't expect to be here 10 years.
"We've won everything, we made the club bigger, and now they [team-mates] are going to take over. This team will have more success, that's for sure.
"I know it's been a bit of a tough year for us but I think this team deserves all the support from you guys. I know they are pushing really hard and this team will be back next year fighting for all the titles."