And another three points for Manchester City, whose winning streak is up to five matches.
That's still not enough to stop Arsenal being top of the Premier League on Christmas Day.
A 1-0 victory at Everton on Saturday, secured by Viktor Gyokeres' first-half penalty, means Arsenal - seeking a first English top-flight title since 2004 - will spend December 25 in first place for the fifth time since the Premier League was formed in 1992.
On none of the four occasions did Arsenal go on to win the title.
History isn't the only thing the Gunners are fighting.
City are just two points behind, and continued their strong recent form by sweeping aside West Ham 3-0.
Haaland scored in each half to move to 19 goals in 17 matches this campaign and also set up Tijjani Reijnders' goal in a 3-0 win at Etihad Stadium.
Haaland has 38 goals in a combined 28 games for club and country.
His double gave him 104 in the Premier League, one more than Cristiano Ronaldo having played 122 games fewer than the former Manchester United icon.
He scored at the second attempt from Phil Foden's cross to give City a fifth-minute lead, then took advantage of a defensive mix-up to make it 3-0 in the 69th.
In between, he slipped a pass to Reijnders, who rifled a shot into the roof of the net in the 38th minute.
City manager Pep Guardiola is still not completely satisfied.
"I said to the players, 'Merry Christmas everyone, but it will not be enough if we don't improve,'" Guardiola said.
Champions Liverpool won at nine-man Tottenham 2-1 but lost record signing Alexander Isak to a left ankle injury sustained when he scored the first goal.
On as a sub against Tottenham, Isak scored within 11 minutes, but in the act of converting his finish, his left ankle was hurt by a challenge from Micky van de Ven and he was helped off the field.
Tottenham were already down to 10 after Xavi Simons' red card for a studs-up foul on Virgil van Dijk.
Hugo Ekitike doubled Liverpool's lead with a header.
Richarlison reduced the deficit for Spurs in the 83rd, but there was still time for Cristian Romero to also get sent off for Spurs after kicking out at Ibrahima Konate.
What a difference a week made for Nick Woltemade. Last weekend, he scored an own-goal to consign Newcastle to a derby loss at Sunderland.
Six days later, he netted twice in the opening 20 minutes against Chelsea. The visitors recovered, though, to draw 2-2 with a free-kick goal from Reece James, before Joao Pedro's equaliser.
Chelsea remained fourth after winning only one of their past five league games.
Basement club Wolves remained without a win and on just two points after losing at home to Brentford 2-0, with Keane Lewis-Potter scoring both the visitors' goals.
It ensured Wolves tied Sheffield United's 2020-21 record of 17 games without a win from the start of a Premier League season.
Bournemouth winger Antoine Semenyo curled home his team's goal in a 1-1 draw with Burnley, who ended a seven-match losing run with a 90th-minute Armando Broja equaliser.
A 0-0 draw at Brighton left Sunderland in sixth place, while Leeds beat Crystal Palace 4-1 to move six points clear of the relegation zone.
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