The win marked the Citizens' fourth consecutive Premier League victory, solidifying their push for a UEFA Champions League spot next season.
Pep Guardiola, City's manager, praised Wolves' relentless intensity. "They are an extraordinary team," he said. "Their shape, quality, physicality, and pace are incredible. We suffered a lot with their chances.
"We were fortunate in some ways, but we did the simple things well after the goal. The result is massively important."
The match was a tale of missed opportunities and fine margins. Wolves came out swinging, with Matheus Cunha and Jean Ricner Bellegarde threatening early. Rayan Ait-Nouri was particularly dangerous, striking the post and seeing a follow-up effort cleared off the line by Josko Gvardiol.
City weathered the storm, and just before halftime, Jeremy Doku's cutback found De Bruyne, who calmly slotted the ball into the bottom corner to send the Etihad into raptures.
Wolves refused to wilt. Cunha hit the post again early in the second half, but City regained control, with Omar Marmoush and Mateo Kovacic going close.
Despite failing to find a second goal, the hosts held firm, extending their home head-to-head winning streak against Wolves to five matches and halting the visitors' six-game winning run.
Guardiola reserved special praise for De Bruyne, whose departure at season's end looms large. "Just thank you," he said. "His contribution, like against Crystal Palace when we were 2-0 down, and today's goal, is immense. It's almost impossible to replace himânot just his performance, but what he means to our fans' hearts. Our success belongs to players like him."
Recent updates from Manchester City's official X account highlighted De Bruyne's impact, noting his "clinical finish" and urging fans to "cherish every moment" of his final games.
Wolves' X posts reflected pride in their performance, with manager Gary O'Neil quoted as saying, "We pushed a top side all the way, but small margins cost us."
With nine points left to play for, City are firmly in the driver's seat for a top-four finish. "It's in our hands," Guardiola said. "Let's go."