The Reds' last-gasp win over Leicester City a day earlier opened up a sizeable lead over Pep Guardiola's side, who were unable to reduce the deficit after an insipid display.
City were second best to their well-drilled opponents for long periods, with Traore's two breakaway goals in the final 10 minutes handing Nuno Espirito Santo's side a thoroughly deserved three points.
The result means the Premier League champions have already lost two of their eight league games this season, while Wolves move up to 11th after just their second win of the campaign.
2 - Adama Traore's second ever Premier League goal has put Manchester City behind in a Premier League match at home for only the second time in their last 26 such matches. Shocked. #MCIWOL pic.twitter.com/KgBjImlnaU— OptaJoe (@OptaJoe) October 6, 2019
Wolves squandered a glorious opportunity to take a fifth-minute lead, Patrick Cutrone skewing horribly wide after being played clean through by Traore.
A sloppy pass from Riyad Mahrez almost cost his side midway through the first half, but two superb blocks by Fernandinho denied Raul Jimenez and Cutrone.
Jimenez then failed to get a shot away quickly enough when bearing down on Ederson after another wayward pass from City, this time from Nicolas Otamendi.
A sluggish City failed to test Rui Patricio inside the opening 30 minutes, although the Wolves goalkeeper did keep out Raheem Sterling and Kyle Walker's efforts from outside the penalty area shortly before the interval.
City went agonisingly close to taking an undeserved lead in the 67th minute when David Silva's wonderful free-kick from 25 yards crashed back off Patricio's crossbar.
Substitute Bernardo Silva saw a goal-bound strike blocked 15 minutes from time – a reprieve that was clinically capitalised on by Traore soon after.
The Spaniard superbly slotted past the onrushing Ederson from Jimenez's pass after an incisive counter-attacking move to stun the home faithful.
The 23-year-old then wrapped up a notable win in stoppage time, again latching onto a Jimenez pass and clipping past Ederson in what was almost a carbon copy of his first goal.
What does it mean? Woeful City hand title advantage to Liverpool
It is still early in the season, but few would argue against Liverpool claiming their first Premier League title since the 1989-90 campaign, given the size of their lead after just eight games. City were abysmal and sorely missed the creative spark of Kevin De Bruyne in the middle of the pitch. Guardiola has a two-week gap now to mastermind a reversal in fortunes for his side and reel in Jurgen Klopp's seemingly unstoppable outfit.
Traore too hot to handle
Premier League defenders know all about the former Middlesbrough winger's pace but for too long his end product has been missing. He was deadly against City, though, producing two finishes that any of City's illustrious attackers would have been proud of.
Otamendi exposed once again
Questions have long been asked of the 31-year-old's suitability for this City side and he showed why with another characteristically uncertain display, which was ruthlessly taken advantage of by Traore.
Key Opta Facts:
- Wolves have beaten Manchester City away from home in a top-flight match for the first time since December 1979, having drawn once and lost six there since then before today.
- Manchester City have lost at home in the Premier League for just the fourth time in 61 matches under Pep Guardiola.
- City have lost a Premier League match at the Etihad Stadium without scoring for the first since March 2016 against Man Utd (0-1), with Manuel Pellegrini in charge.
- Wolves have beaten the reigning champions of the top-flight away from home for the first time since January 1984, when they defeated Liverpool 1-0 at Anfield.
- Adama Traore had not scored in his last 32 Premier League games before netting twice against Man City today, last scoring against West Ham in September 2018.