Declan Rice scored again to help West Ham end the perfect week with a vital 4-0 win at Bournemouth to boost their survival chances. The Hammers fought back from two down to draw with Premier League leaders Arsenal last Sunday and followed it up with a 4-1 victory over Gent on Thursday to book their spot in the Europa Conference League semi-finals. Relegation has remained a distinct possibility for David Moyes’s side though, but they eased those concerns with a clinical display in which first-half goals by Michail Antonio, Lucas Paqueta and Rice put them in control. Substitute Pablo Fornals added a fourth midway through the second half to help West Ham move up to 13th and six points clear of the bottom three. Despite their exploits on Thursday, Moyes only made two changes at the Vitality Stadium and one was to recall first-choice Lukasz Fabianski in goal. It meant Antonio got another opportunity to lead the line and he rewarded his manager’s faith with a fifth-minute opener. Bournemouth made it far too easy for the Hammers, with Aaron Cresswell’s near-post corner powered home by the unmarked Antonio for his 12th goal of the season, but only his fourth in the league. West Ham doubled their advantage eight minutes later and again it would have frustrated Cherries boss Gary O’Neil. Vladimir Coufal won back possession from Marcus Tavernier and controlled Jarrod Bowen’s pass before his looping cross was headed in at the back post by Paqueta, who easily outjumped Jack Stephens. It continued Paqueta’s encouraging form since the World Cup break and backed up his goal-scoring display in Thursday’s triumph over Gent. West Ham’s travelling support were enjoying their trip to the south coast and soon singing about rivals Tottenham, who were 5-0 down at Newcastle inside 21 minutes. But Bournemouth were not prepared to throw the towel in and Chris Mepham tested Fabianski with a header moments later. Jefferson Lerma was next to try his luck and Fabianski was again equal to it but his best stop was to come next. Dominic Solanke muscled his way past Nayef Aguerd and raced into the area but Fabianski saved well with his feet to preserve West Ham’s two-goal lead after half an hour. Having withstood Bournemouth’s fightback, Moyes’s side then provided a sucker-punch two minutes before half-time through their talisman. Another Cresswell corner caused problems and, while it was cleared to the back post, Rice was first to the loose ball and on hand to drill home via a deflection to make it back-to-back goals this week. The Hammers captain was serenaded by the away fans soon after with chants urging him to stay amid talk his future could lie away from the London Stadium after this campaign. O’Neil responded with Wales forward Kieffer Moore introduced in place of Joe Rothwell at half-time but it failed to have the desired effect. A triple substitution followed on the hour mark for Bournemouth with Dango Ouattara, the stoppage-time hero at Spurs last weekend, brought on and while he initially caused problems, West Ham were soon celebrating a fourth goal. Bowen did well down the right and, while his cross was slightly behind Fornals, the substitute managed to back heel into the far corner to make it 4-0 after 72 minutes. Hammers substitute Maxwel Cornet had a stoppage-time effort ruled out for offside and the West Ham fans finished the game chanting for Rice to stay one more year with this win at least going a long way to confirming their place in the Premier League next season. After the game, Rice said: "I'm scoring again, two in a row, back-to-back. There have been a lot of question marks over my scoring ability. A few games to go and hopefully I can keep notching. "That's the first time we scored within 15 minutes all season. I thought we saw it out really well and think we saw a team pushing to get out of where we are in the table. "The benchmark for [staying in the Premier League] in a standard season is 40 points, so it is important we don't get too comfortable. We have Liverpool next and we relish those kind of nights." Meanwhile, Bournemouth, who have now dropped to 15th, will aim to quickly regroup for the trip to rivals Southampton on Thursday.