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Kompany scored with a thunderous long-range strike to decide their penultimate league match of the season against Leicester City, a key moment in their retaining the Premier League title.
It was a good result for Wolverhampton Wanderers too as they will now qualify for the Europa league via their seventh-place finish in the Premier League.
The Merseyside club ended their league campaign one point behind champions Manchester City, who sealed a second successive title by coming from a goal down to beat Brighton and Hove Albion on Sunday.
Manchester City's 98 points and Liverpool's 97, with third-placed Chelsea a further 25 points adrift, certainly illustrate just how relentlessly successful the top two were.
The victory was the 12th win in a row for City, who have shown no signs of giving Juergen Klopp's Liverpool, who have lost just once all campaign, the slightest opening.
City fans had celebrated what looked like the goal that sent them into the last four before the replay confirmed that Sergio Aguero was offside in the build-up.
With the result in the balance until the end and City desperate to cling on to all three points, the final stages were nervous.
With Spurs talisman Kane having hobbled off injured and favourites City beginning to turn the screw, Son sent the home fans inside the London club's majestic new stadium into delirium as he fired past Ederson in the 78th minute.
City have 89 points, one more than rivals Liverpool, with both teams having three games to play - and none of them against top six opponents.
Salah and Mane now have 21 and 20 goals each this season -- making them the top two scorers in the Premier League.
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