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 after 37 games.
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, AFP reported.
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.
"We gave the chance in our hands for the last game," Guardiola told the BBC. "The tennis players say 'The serve to win Wimbledon, the last game, is the most difficult one'.
"It happened in our period against Aston Villa (in 2022). And many, many years ago it happened with Sergio Aguero (scoring) in 93 minutes 20 seconds against QPR. So there will be the typical game."
Guardiola called for help from City's fans to get them over the line.
"We know what we're playing for," he said. "The tension is there, the rival is so good. It's why it is difficult, we know that.
"Everyone come to the stadium and make noise. These games are more difficult but you have to do it. We'll have one day off, two days to prepare, and then we will do our best."
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's 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.
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 faithful 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.
