Pep Guardiola's side needed to respond to leaders Arsenal's comfortable victory over Bournemouth earlier in the day and they did so emphatically, with a clinical take-down of their hapless visitors at the Etihad Stadium.
Haaland struck twice from the penalty spot in the first half, either side of a towering header, before adding a fourth with a stunning strike.
Substitute Julian Alvarez also got on the scoresheet, while Wolves' consolation came from Hwang Hee-chan.
The victory lifted City, chasing an unprecedented fourth successive league crown, back within a point of the Gunners with a game in hand.
Haaland's outstanding display took his tally for the campaign to 36 in all competitions and lifted him to 25, five clear of his nearest challengers, in the race for the Premier League's Golden Boot. His hat-trick was also his ninth in City colours.
City will be assured of the crown if they win their three remaining league matches, all against London opposition. They go to mid-table Fulham next Saturday, visit Tottenham the following midweek and finish with a home match against West Ham on May 19.
Earlier in the day Arsenal have maintained their pursuit of the Premier League title with a 3-0 win over Bournemouth.
Bukayo Saka converted a penalty in the 45th minute after a trip on Kai Havertz before Leandro Trossard and Declan Rice added second-half goals at Emirates Stadium to secure Arsenal's fourth straight victory in the league.
Arsenal, seeking a first league title since 2004, have two matches still to play, at Manchester United and home against Everton.
