The game, played in wet and windy conditions, looked to be heading for a goalless conclusion at Vitality Stadium.

Philip Billing had a header tipped on to the bar by Henderson while at the other end Eberechi Eze's goal celebrations were cut short by an offside flag after the Palace player had finished from six yards.

But Kluivert's 79th-minute winner proved the difference and lifted his side up to 11th in the table.

Cherries moving in right direction

Bournemouth find themselves in an unfamiliar but very welcome position of being all but safe eight games from the end of Andoni Iraola's impressive first season in charge.

Billionaire club owner Bill Foley said in December he is confident the club can qualify for Europe within five years

and that they should take inspiration from Brighton.

The Cherries have 41 points and have already surpassed last season's tally of 39.

They are seven points behind sixth-placed Manchester United and are eyeing a top-half Premier League finish for only the second time.

Such is the feel-good factor around the club that Iraola was even asked whether his side could sneak into Europe after his side's latest success.

"No. The only thing with 41 points is that you know you are safe and are going to be in the Premier League next season," he said.

"We have smaller goals. It's good to be not so far from teams in the top 10."

On a dreadful night weather-wise on the south coast, Bournemouth had to wait until late in the game to get the winner.

Henderson, deputising for injured first-choice keeper Sam Johnstone, had already produced a fine save to keep out Billing's header while Lloyd Kelly headed another great chance wide.

The closest Dominic Solanke came to adding to his 16 Premier League goals was when he fired into the side netting in the second half.

But Netherlands forward Kluivert sent fans home happy after great work by Semenyo.

Five of Bournemouth's remaining eight games are away from home, including tough-looking matches at title-chasing Arsenal and Champions League hopefuls Aston Villa.

They are unlikely to hold much fear for Iraola's side, who are building confidence and momentum with an unbeaten Premier League run that stretches back to 24 February.

Familiar pattern for Palace

Four months have passed since Crystal Palace supporters booed their own players off the pitch after a 2-0 home defeat by Bournemouth while an object was launched by a fan in the direction of then-manager Roy Hodgson.

Palace have won just three Premier League matches since - losing seven - while they have replaced Hodgson with Oliver Glasner.

"If you don't score a goal you can't win," said the Austrian after his side's latest defeat. "We had many good situations. You need to shoot. Maybe we have to improve, be more decisive in offensive positions."

With Joel Ward making his 300th top-flight appearance for the club, the Eagles were on their way to securing a hard-earned point when they conceded another late winner.

It has been a familiar pattern. Palace led 1-0 at Aston Villa back in September before letting in three late goals, while as recently as 9 March they had to make do with a point at home to Luton after conceding in the 96th minute.

Palace remain eight points above the relegation zone but it is now just one win in eight, with a tough match at home to Treble-chasing Manchester City coming up on Saturday (12:30 BST).