The 23-year-old marked his return from injury with a second-half strike less than 10 minutes after coming on as a substitute in City's 2-0 win at Nottingham Forest last weekend, and he only needed 12 minutes to open the scoring against Wolves.
Haaland confidently converted from the penalty spot to put City ahead after referee Craig Pawson deemed that Rayan Ait-Nouri had clattered into Josko Gvardiol inside the area - a "terrible" decision from the officials according to Wolves boss Gary O'Neil.
City's No.9 then powered a superb header into the far corner, before completing his hat-trick on the stroke of half time with another penalty after Nelson Semedo brought him down inside the box with a late challenge.
Wolves pulled one back through Hwang Hee-chan shortly after the interval, but Haaland scored his and City's fourth less than a minute later, whipping a brilliant left-footed shot into the far corner, before Julian Alvarez completed the rout with a low-driven shot five minutes from time to keep City's title hopes alive.
Haaland responds to Keane's "League Two" comments
Although Haaland has scored 25 Premier League goals this season, at least five more than his nearest challengers, the Norwegian has received criticism from some quarters over his performances this season.
Following City's goalless draw with Arsenal earlier this year, Sky Sports pundit and ex-Man United midfielder Roy Keane claimed that Haaland's general play was "so poor" and likened the striker to "a League Two player".
Since then, Haaland has scored seven goals in his last six appearances for City in all competitions, albeit four in his most recent outing against Wolves, and the striker has now responded to Keane's comments for the first time.
"I don't really care that much about that man, so that's all right," Haaland told Viaplay. "I don't care, we just have to win our games and now, relax tonight and focus on Fulham."
Keane has history with the Haaland family after he injured Alfe-Inge Haaland with a nasty stud-showing tackle during a Manchester derby back in 2001 - Alfe-Inge's career was ultimately never the same after that incident.
Haaland 'on a mission' to fire City to another title
Haaland is one of only three players in Premier League history, after Andrew Cole and Michael Owen, to score two first-half hat-tricks in the division, with his treble against Wolves preceded by three goals scored in a 6-0 win over Nottingham Forest last season.
The Norwegian scored his fourth goal against Wolves in the 54th minute; only ex-City man Gabriel Jesus - now at Arsenal - can better that, as he netted four times in 53 minutes versus Watford in April 2022.
Haaland has now scored 36 goals in 41 appearances for the Citizens in all competitions, including 25 in 28 Premier League games, and the Golden Boot-chasing striker has stressed that he is focused on ending the season strongly as Pep Guardiola's side endeavour to retain the title.
"Feels fantastic to score four goals, [and an] important win," Haaland said as quoted by mancity.com. "It was a difficult game, [Wolves] can play football so it was not easy, but we were solid and we were on a mission, we're so focused on the game and now we focus on the next one."
Man City, who sit just one point behind leaders Arsenal with a game in hand, will travel to Craven Cottage for their next Premier League fixture against Fulham on May 11, before ending the campaign with a trip to Tottenham Hotspur and a home encounter with West Ham United.