The Norwegian forward tapped home a pinpoint Kevin De Bruyne cross early in the second half to score City's first-ever league goal at the Tottenham Hotspur Stadium.
And he netted a late penalty to seal the three points for the visitors, minutes after substitute goalkeeper Stefan Ortega saved brilliantly from Son Heung-min.
The win takes Pep Guardiola's team two points clear of Arsenal at the top of the table.
Victory at the Etihad against West Ham on Sunday will make them champions for a fourth consecutive season, regardless of the Gunners' result against Everton.
No team in English top-flight history has ever won four titles in a row.
Defeat for Spurs also guarantees that Aston Villa will finish in the fourth Champions League spot, joining City, Arsenal and Liverpool in Europe's top-tier competition next season.
But City defender Kyle Walker warned the job was not done yet.
"We prepare, we recover and West Ham is another final and hopefully we can go and make history for this great club," he told Sky Sports.
"It is not job done by a million miles. Hopefully, we can get the win. If I didn't enjoy the pressure, I would be in the wrong job and the wrong team.
"Last night, I couldn't sleep. They tried to set fireworks off but we weren't there, they missed us. I can't describe the feeling when we went 2-0 up."
The build-up to the game in north London was dominated by a fierce debate over whether home fans wanted their own team to lose in order to leave City in the driving seat, with Arsenal their nearest challengers.
The Spurs supporters made their feelings towards their bitter local rivals clear in the opening minutes, with chants of "Stand up if you hate Arsenal" ringing around the stadium.
Tottenham had the first sight of goal, with City goalkeeper Ederson tipping over a fierce Rodrigo Bentancur effort before Spurs goalkeeper Guglielmo Vicario kept out Phil Foden's close-range shot.
City, who came into the match unbeaten in 21 league matches, were short of their fluent best while Spurs struggled to put the finishing touches to their attacking moves.
City break deadlock
Moments after the re-start Vicario dived full length to keep out a stinging De Bruyne effort.
But the visitors broke the deadlock in the 51st minute when Bernardo Silva found De Bruyne in the box and the Belgian crossed for Haaland to slot home from point-blank range.
Thousands of Spurs fans chanted "Are you watching Arsenal" as the City fans celebrated in their corner.
The game then became disjointed as De Bruyne was raked down the Achilles by Pape Sarr before Ederson took a blow to the head in denying Cristian Romero and was replaced shortly afterwards by Ortega.
The German was called into action immediately, denying substitute Dejan Kulusevski from close range.
Time stood still when Son burst through with five minutes of normal time remaining but Ortega saved with his legs when the South Korean seemed certain to score.
Guardiola fell to the ground, clutching his head in disbelief.
Instead City were awarded a penalty when Pedro Porro brought down substitute Jeremy Doku and Haaland smashed home in the 91st minute to spark wild celebrations from the players in front of the City faithful, taking his league tally to 27 goals for the season.
Last year's treble winners will prepare for Sunday's finale knowing they stand just 90 minutes away from creating another slice of football history.
