The Cherries appeared on course for victory after Harry Arter opened the scoring with 17 minutes gone on the south coast. But Dimtri Payet hauled the visitors level with a magnificent free-kick shortly after the hour mark, before Enner Valencia netted twice to see West Ham triumph 3-1 – their third consecutive league victory. Benik Afobe, the £10million signing from Wolves, was Eddie Howe’s only change from his side’s 0-0 draw at Leicester, with fellow new arrivals Lewis Grabban and Juan Iturbe were on the bench. Payet made his first start for the Hammers in over two months, while Pedro Obiang kept his place in the visitors’ starting XI following their 1-0 victory against Wolves in the FA Cup. In Bournemouth’s first Premier League game under the lights, it was West Ham who enjoyed the best of a scrappy opening. Mark Noble blazed his effort over after a sloppy header from Simon Francis, before the Bournemouth defender made amends with a good clearance underneath his own bar following fine work from Andy Carroll on the right. It was to be the injury-prone forward’s last contribution. The 27-year-old, making only his seventh league start of the season, was left on the floor holding his left leg after just 12 minutes and moments later was hobbling down the tunnel shaking his head with his match over. How long he will be sidelined for this time remains a mystery, but West Ham boss Slaven Bilic soon had more pressing matters when Bournemouth took the lead after 17 minutes. Arter let fly from 20 yards and goalkeeper Adrian, diving low to his right, could only palm the ball into his own net. The Republic of Ireland midfielder was celebrating his first Premier League goal and suddenly the momentum was with Bournemouth. Afobe, who scored 23 goals in 48 games for Wolves, headed over the bar from six yards, before Charlie Daniels’ fizzing effort was palmed away by Adrian. Afobe then found himself with only Adrian to beat after a fine through-ball from Junior Stanislas, but the former Arsenal striker fluffed his lines and a grateful Adrian collected the ball. On the stroke of half-time Artur Boruc was at full stretch to tip Payet’s shot over the bar to ensure the Cherries headed into the interval with the advantage in what was the visiting side’s first real effort on goal. After the break, Bournemouth seemed content to sit back and it was West Ham who enjoyed more of the ball, but without the goal threat of Carroll failed to test Boruc. That was until Payet’s moment of magic shortly after the hour mark. His curling free-kick left Boruc with no chance and his effort crashed in on the underside of the bar. West Ham were buoyant and they took the lead seven minutes later after the brilliant Payet teed up Valencia, who could not miss from eight yards. Bournemouth were left stunned and they failed to muster a clear chance in the remaining 16 minutes. Indeed it was Valencia who put the icing on the West Ham cake, with the second brilliant free-kick of a fine night for Bilic’s men. TWEET OF THE MATCH “3 outstanding goals, you won’t see many better all season, top class 2nd half performance. #BOUWHU #COYI” – Matthew Etherington was impressed by his former club’s display at Bournemouth RATINGS Bournemouth Artur Boruc 6 Simon Francis 5 Steve Cook 5 Dan Gosling 6 Andrew Surman 5 Harry Arter 6 Charlie Daniels 6 Adam Smith 6 Matt Ritchie 5 Junior Stanislas 6 Benik Afobe 5 Subs: Juan Iturbe 5 Lewis Grabban 5 Glenn Murray 5 West Ham Adrian 5 Aaron Cresswell 5 James Tomkins 5 James Collins 6 Michail Antonio 6 Mark Noble 7 Pedro Obiang 7 Angelo Ogbonna 6 Dimitri Payet 8 Enner Valencia 8 Andy Carroll 5 Subs: Nikica Jelavic 5 Carl Jenkinson 5 Alex Song 5 STAR PLAYER Dimitri Payet: How West Ham have missed the Frenchman. In his first start in over two months, Payet hauled the Hammers level with a David Beckham-esque free-kick before turning provider moments later to tee up Enner Valencia. MOMENT OF THE MATCH Andy Carroll probably can’t believe his luck. Bidding to score in his third successive Premier League match for the first time in his career, the England international lasted just 12 minutes at the Vitality Stadium before succumbing to yet another injury. VIEW FROM THE BENCH Slaven Bilic has spent much of his short West Ham career fielding questions about Carroll’s fitness and it will be on the agenda for the Hammers boss once more after the forward’s injury here. Bilic turned away with a grimace and kicked a Lucozade box when it became apparent that Carroll could no longer continue. MOAN OF THE MATCH Payet was shown a yellow card by referee Martin Atkinson for apparently over-zealous celebrating with the West Ham fans. It seemed harsh. NEXT UP Bournemouth v Norwich (Barclays Premier League, Saturday, January 16) Newcastle v West Ham (Barclays Premier League, Saturday, January 16) Press Association West Ham scored three goals in 17 second-half minutes to secure a fine comeback victory at Bournemouth in the Barclays Premier League on Tuesday night.