A 2-1 victory at Anfield means Arne Slot's team need to win just two more games to be certain of a record-equalling 20th English league title to draw level with Manchester United's total.
"A big relief," was how the Liverpool manager described Van Dijk's 89th-minute header. "We saved a big set-piece for a very important moment."
Liverpool had looked like dropping points when Andy Robinson scored an own goal in the 86th minute to level the game at 1-1 after Luis Diaz's opener.
The Merseyside club are now 13 points clear at the top of the standings with six rounds to go and could be crowned champions as early as next Sunday if Arsenal lose to Ipswich earlier that day..
Victory completed a week of celebrations for Liverpool supporters after top scorer Mohamed Salah ended uncertainty over his future by signing a new two-year contract.
He marked that new deal in style by maintaining his outstanding form this season to cross for Diaz's opener in the 18th minute.
It was his 45th goal or assist in the league this season, which set a new record for a 38-game Premier League campaign.
West Ham twice came close to equalising before Robertson's own goal. Mohammed Kudus hit the bar in the first half and Jarrod Bowen was denied by Alisson when through on goal after the break.
Elsewhere, Andre Onana was left out of Manchester United's squad for the game against Newcastle following his latest high-profile errors for the club - but it didn't prevent a 4-1 loss for Ruben Amorim's team at St James' Park — a 10th defeat in 21 Premier League games since he took charge in November.
Two goals from Harvey Barnes helped condemn United to a guaranteed new club record for their lowest points haul in the Premier League era -- an unhappy way to mark Man United's 4000th game in the English top-flight.
Wolves earned a 4-2 home victory over Tottenham, heaping more misery on Ange Postecoglou and his team.
Rayan Ait-Nouri struck after only two minutes before Djed Spence's own goal seven minutes before half-time left the visitors with an uphill battle at Molineux.
Mathys Tel pulled one back for Spurs, only for Jorgen Strand Larsen to swiftly make it 3-1, and then Richarlison's consolation was quickly followed by a fine individual effort from the available again Matheus Cunha to secure a triumph which moved Wolves up to 16th.
Spurs are one place higher after a 17th league loss of the campaign, days out from a make-or-break Europa League quarter-final second leg at Eintracht Frankfurt.
Chelsea dropped potentially precious points in the battle for Champions League qualification as they were held to a 2-2 draw at home to Ipswich.
A breakaway goal by Julio Enciso put the struggling visitors ahead after 19 minutes and Ben Johnson's header just past the half-hour mark helped Kieran McKenna's team establish a two-goal advantage.
An own goal by Axel Tuanzebe immediately after the interval gave Chelsea hope and, while Jadon Sancho curled home a sumptuous leveller 11 minutes from time, the shares were spoiled to leave the Blues in fifth place.
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