When Mauricio Pochettino sits down with Chelsea’s board for the review that will determine whether he continues as head coach, perhaps he can point to the fact that he has imbued his collection of young talents with so much confidence that European football was secured in part thanks to Moisés Caicedo scoring from halfway.

It turns out that this is what £115m buys these days: ­crunching tackles, perceptive passing and a goal of the season contender.

Yet before merely looking at the extravagance of the spending, it is worth remembering that it has taken ­Pochettino’s ­coaching to knit ­everything together.

Related: ‘My phone is going to be on’: Mauricio Pochettino in dark over Chelsea future

Pochettino refused to say whether he received assurances on his future from Todd Boehly after going out for “a very nice dinner” with Chelsea’s co-owner last Friday.

This entertaining 2-1 win against Bournemouth was further proof that Chelsea, who will play in the Europa League rather than the Europa Conference League if Manchester City beat Manchester United in the FA Cup final, do not need more upheaval.

There are hints of unity at Stamford Bridge. Nobody was booing Raheem Sterling when he scored the goal that secured sixth place for Chelsea, while Caicedo’s improvement since his move from Brighton last summer is evidence of the plan coming together. The midfielder started the campaign slowly and ended it by embar­rassing Bournemouth’s goalkeeper, Neto, with his astonishing goal.

Chelsea being Chelsea, though, there would still be flashes of ­defensive frailty for Pochettino’s bosses to consider. Bournemouth, who ­finished 12th in an impressive debut season for Andoni Iraola, halved the deficit through Benoît Badiashile’s own goal and should have completed the fightback in added time. ­Dominic Solanke could not believe that he fired over an open goal after Djordje Petrovic saved from Dango Outtara. Behdad Eghbali, José E ­Feliciano and Todd Boehly, ­Chelsea’s ­co-controlling owners, may have wondered why ­Bournemouth were given so much space to ­counterattack in the 94th minute.

Manchester City Champions League

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Chelsea Europa League if Manchester City win the FA Cup; Europa Conference League if Manchester United win the FA Cup

Newcastle Europa Conference League if Manchester City win the FA Cup; not in Europe if Manchester United win the FA Cup

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Supporters reading the matchday programme will have found a long message from the ownership group that talked about needing to be “consistently winning or contending for the Premier League” and “­consistently playing in the Cham­pions League”. Maybe Pochettino’s failure to come close to reaching those targets this season explains why he did not merit a mention in the entire piece.

Even so, the Argentinian can point to finishing above Newcastle and United after five consecutive wins. Hitherto disgruntled fans are seeing ­pulsating football and watching a defensive midfielder whose skillset is not ­confined to his ball-winning ability.

Chelsea were dominant before Caicedo’s opener in the 16th ­minute. Bournemouth were pushed back, Nicolas Jackson and Cole Palmer spurning early opportunities after fine work from the dangerous ­Sterling, and the breakthrough was not simply down to individual brilliance. As inspired as Caicedo’s moment was, the move had started with Jackson spinning and sending Sterling through on goal.

Because of what followed, ­Chelsea were grateful that Jackson’s pass was marginally overhit. Neto flew out of his area, produced a fine tackle and prepared to clear, only to scuff the ball towards the halfway line because of sudden pressure from Conor Gallagher.

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Caicedo, as he tends to be, was waiting. Urged to shoot by the crowd, he crept a couple of yards into Bournemouth’s half and channelled his inner David Beckham. Neto was stranded as the ball sailed over him and dipped under the bar before Marcos Senesi could head clear.

Perhaps liberated by such a school’s out goal – Caicedo’s first for the club – an air of silliness gripped both teams. Chelsea became ­slapdash, their early intensity fading. Marc Cucurella and Antoine ­Semenyo were booked after a clash. Milos Kerkez was punished for diving. Bournemouth ­threatened through Marcus Tavernier and Ryan Christie.

Chelsea needed to wake up, particularly when Enes Unal missed another inviting chance at the start of the second half. They responded when Palmer combined with Sterling, who drove into the area and scored with a shot that went in off the luckless Neto.

It should have been game over. Bournemouth, who started Solanke on the bench due to a hip issue, decided otherwise when Cucurella allowed Kerkez’s cross to reach Unal in the 49th minute. The striker’s weak shot struck Badiashile and looped over Petrovic.

There would be no clean sheet for Silva before he joins Fluminense. It became nervy, Solanke shooting wide after coming on and Petrovic denying Christie before the late drama.

Chelsea survived and finished on a high. The question is what comes next. There was no sign of ­Pochettino engaging with the crowd after full time. He stayed to watch the emotional farewell to Silva, but headed straight down the tunnel before the players went on a lap of appreciation.