Bournemouth took a significant step towards Premier League survival with a precious win which pushed rivals Southampton closer to relegation.Marcus Tavernier claimed the Cherries' second-half winner at a soggy St Mary’s to move the Cherries seven points clear of the drop zone and pile further pressure on the division’s bottom club.Beleaguered Saints thought they had snatched a dramatic 89th-minute equaliser but Che Adams’ effort was ruled out for offside following a VAR review.The hosts lacked attacking thrust and urgency for much of a miserable evening as they slipped to a club-record 11th home league defeat of the season following a largely-feeble display.Ruben Selles’ side, who lost captain James Ward-Prowse to illness at half-time, go into their final five games of a dismal campaign six points from safety and with lingering hopes of survival fading fast.A painful defeat to their near neighbours stretched Saints’ alarming winless run to eight games to eradicate any positivity generated by Friday’s thrilling 3-3 draw at leaders Arsenal.Southampton forward Adam Armstrong struck a post early on but, aside from Adams’ disallowed finish, the troubled hosts offered little after falling behind to the 50th-minute goal from Tavernier, who later limped off injured.Bournemouth made the 30-mile journey east seeking a third-successive away win to increase their cushion on the drop zone and with the prospect of being the region’s top club next term.Cherries fans wasted little time in taunting their struggling rivals as chants of 'Oh when the Saints go Championship' frequently rang around the stadium.The precariously-placed home team did their best to quell the constant crowing in the early exchanges.Theo Walcott tested Neto with a