An overdue three points will offer Frank Lampard no end of comfort but there is a danger the scoreline will sugarcoat a lukewarm performance in a much-needed victory. Two goals in the closing stages, from Benoît Badiashile and the substitute João Félix, earned Chelsea a first win in 10 matches to extinguish any lingering concerns of suffering another humbling. The sarcastic chants emanating from the away end after Conor Gallagher’s opener and again at full-time said everything about a trying few weeks. “We are staying up,” the travelling supporters sang. Lampard was unmoved when Gallagher headed Chelsea in front early on but the interim manager allowed himself the smallest of celebrations when Félix stroked in Chelsea’s third goal with four minutes of normal time left to play. Lampard gravitated towards the touchline as he clenched both fists and his assistant, Joe Edwards, jumped from the dugout to join him. At the final whistle Lampard walked over to the away supporters who bookended this win by singing his name. “I appreciate their support,” he said. “We had a moment at the end where everyone feels good for a day. Today was a nice small step forward.” It was hardly all sunshine and roses for Chelsea and it has not been for a while. A section of their supporters booed the second-half arrivals of Hakim Ziyech and Raheem Sterling and at another point they made their feelings plain about Todd Boehly, the under-fire Chelsea chairman who is gaining caricature status by the week and whose £600m investment continues to show little return. April was so bleak for Chelsea – they scored one goal in a run of six defeats in seven games – that their in-house goal of the month competition only featured players from the academy and women’s teams. No wonder Lampard said his players would savour the victory. “When you don’t have that feeling for a while, it gradually knocks you down,” he said. “The lads are human. We’re all affected in similar ways when you’re not winning games. The only way to get through that is to work through it. It will make the players stronger as they go on. “They should enjoy it, have a beer, have a glass of wine and do whatever they do, but we cannot take our foot off the pedal in terms of taking steps forward until the end of the season.” A top-half finish is not yet out of reach for Chelsea – how the mighty have fallen – who have to play Manchester City, Manchester United and Newcastle. Changes were inevitable for Chelsea given the manner of their defeat at Arsenal in midweek, with Badiashile one of five players promoted to the starting lineup. Wesley Fofana was missing with a hamstring complaint and Pierre-Emerick Aubameyang left out altogether. Mykhailo Mudryk also started but the £89m signing’s only memorable contribution was a first-half dive that earned him a yellow card. Kai Havertz was equally ineffective. Few of Chelsea’s starters came out of this game with any credit. An in-form Bournemouth proved awkward opponents and they missed chances to seize the lead in the second half, after Matias Viña cancelled out Gallagher’s header with a brilliant curled shot that nestled in the far corner of Kepa Arrizabalaga’s net. Dango Ouattara sent a free header over the bar after Jefferson Lerma kept a corner alive and Arrizabalaga also saved smartly to deny Viña, the Roma loanee, a second goal. “To suffer a 3-1 loss makes it look like a comfortable win for Chelsea, but it was never that,” said the Bournemouth manager, Gary O’Neil. Lampard’s substitutes ultimately turned the tide. The away supporters jeered his decision to replace Noni Madueke with Ziyech but the latter fashioned Chelsea’s first real chance of the second half and teed up Badiashile for their all-important second goal. And Sterling supplied Félix for Chelsea’s third. First, an unmarked Havertz failed to direct his header on goal after rising to meet Ziyech’s cross but Badiashile had no such problem finding the target, feasting on some slack defending to prod in Ziyech’s free-kick. The substitute Félix then eluded his marker, Lerma, to side-foot Sterling’s cutback into the bottom corner to seal a welcome victory.