Stanislas gave the Cherries a first-half lead, but that was wiped out with seven minutes left as Burnley equalised through Sam Vokes.
However, King struck two minutes later to extend his side's recent unbeaten run to four matches and move the club back into the top half of the standings.
Read below to see how the action unfolded at the Vitality Stadium.
2.01pmHello, and welcome to Sports Mole's live coverage of the match in the Premier League between Bournemouth and Burnley.
2.05pmAt the start of the season, both Bournemouth and Burnley would have accepted securing their place in next year's Premier League on the final day of the campaign but their results have already enabled them to relax. Not only that, both teams have ambitions of finishing in the top 10 when all is said and done next Sunday.
2.08pmLATEST! Before we continue, I will bring you an update on the match involving Manchester City and Leicester City because we have just witnessed a brilliant piece of refereeing. Riyad Mahrez thought that he had netted with a penalty to make it 2-2, but he slipped and contacted with the ball twice, which was spotted by the official. It remains 2-1, and you can follow the closing stages by clicking here.
2.12pmWithout further ado, let's get cracking with the team news coming from the Vitality Stadium...
2.15pmBURNLEY SUBSTITUTES: Flanagan, Brady, Gray, Defour, Gudmundsson, Darikwa, Pope
2.19pmTo make things much more concise, we are going to round up both sets of teams here. Why? Both sides are unchanged from their last match. It comes as a bit of a surprise, with both teams only drawing in home fixtures with West Bromwich Albion and Stoke City respectively, but it means that we get to see how Lys Mousset plays in his second successive league start for Bournemouth, and how Burnley cope with both Michael Keane and Ben Mee.
2.24pmHEAD TO HEAD! Today's match represents just the 26th time in which these two clubs have faced each other in a competitive fixture, with Burnley claiming 10 victories in comparison to four wins for Bournemouth. The Cherries have failed to prevail in any of their seven previous contests with the North-West outfit, a run stretching back to 1998, but they ran Burnley close in the reverse fixture at Turf Moor back in December.
2.29pmOn that occasion, Burnley ran out 3-2 winners thanks to goals from Jeff Hendrick, Stephen Ward and George Boyd. Benik Afobe and Charlie Daniels scored for the visitors at the end of each half but it was not enough to stop Burnley adding another three points at their home ground. To look back at that fixture, click here.
2.32pmRESULT! The full-time whistle has gone at the Etihad Stadium and Manchester City have just about held on to claim a 2-1 victory over Leicester City. It is a result which takes them into third place, and could be enough to seal a spot in next season's Champions League. Click here to read our on-the-whistle report.
2.38pmBournemouth boss Eddie Howe would have been disappointed that his side failed to beat Stoke City last weekend, but the main positive was that he witnessed his team twice come from behind to earn a share of the spoils. It also meant that they extended their unbeaten record to three matches ahead of a winnable match this afternoon and a trip to Leicester City on the final day of the season.
The aim will be to at least match the points tally of eighth-place West Brom, but with the Baggies still having to make the trip to the Etihad Stadium to play Man City, their goal difference could take a hit and give Bournemouth a chance to finish above them, providing that they win on the south coast today.
2.43pmEight points from half-a-dozen matches means that Burnley don't match Bournemouth's recent form, but that is not to say it has not gone down extremely well at Turf Moor. Sean Dyche has worked wonders at the club and picking up points in each of their last four matches against teams outside of the top seven has led to them comfortably achieving survival. The biggest plus point during that period was the 2-0 win away at Crystal Palace because it marked their first away success all season. Burnley will have to improve on their travels next season but for now, they can look back at a tremendous first year back in the Premier League.
2.50pmMuch has been made of Bournemouth's rise up the English football pyramid - they only won promotion from League Two in 2010. If they can win today, they would be in pole position to finish in the top 10 and aside from Leicester City's fairytale Premier League title win, has there been another story as remarkable as Bournemouth's? Of course, they still have work to do but if they can achieve their target - as well as complete the reported signings of John Terry and Jermain Defoe - what next?
2.53pmPREDICTION! While Burnley will take belief from their success away at Palace, we can't back against Bournemouth this afternoon. We have got a feeling that this could be a goal-fest, given that the pressure is off both teams. It may seem bold, but we are going for Bournemouth to prevail by a 4-2 scoreline.
2.58pmIt's time for the two clubs to make their way out on the south coast. Kickoff for this one is coming right up. We will keep you up-to-date with the other two 3pm kickoffs as much as we can.
1 minSHOT! Well that didn't take long. Burnley show their intent by attacking straight from the kickoff but Boyd's weak effort went wide of the post.
3 minBack come Bournemouth, who show their own intent by launching a rapid move involving King and Stanislas but they were unable to find Mousset who was closer to goal.
7 minIt is still early days but it remains goalless in the other matches in the Premier League. Both teams will be hoping that Middlesbrough can cause a surprise and get a win over Southampton, who are also vying for a top-10 position.
10 minScratch that - we have a goal, and it has gone to Swansea! Fernando Llorente has given the Welsh side the lead at Sunderland and as it stands, they are going four points clear of the relegation zone!
Back to this game, and while there is a lot of huffing and puffing, no chances are coming from it.
14 minWe have not seen much of Mousset so far. This is a big game for the young Frenchman. He hasn't really been given the chance to make an impact since signing for the Cherries last summer, so he needs a good performance today.
18 minWhile Mousset doesn't necessary offer too much of a threat for Bournemouth, he gives them pace, like the majority of their players going forward. King and Stanislas look as threatening as ever but for now, they are struggling to pick out their targets when they get into the final third.
23 minIs it possible to retract my earlier prediction? No? Worth a try.
Vokes has just got a tame header on target but it was never going to beat Boruc in the Bournemouth goal. As you were in this one...
26 minBournemouth take the lead and it is former Burnley winner Stanislas who has got it. The goal is made by Lewis Cook - who has had to remain patient this season - with the midfielder's pass being controlled by his teammate who produces a clinical finish past Heaton.
30 minBased on the pattern of the game, Burnley probably deserve to be ahead but that was the first time they had got a decent effort away on goal. However, Vokes is starting to offer more of a threat up the other end of the pitch.
34 minSHOT! This is much better from Burnley. Arfield has remain on the periphery of the game but he has just tried his luck from distance, with the strike going just wide of Boruc's goal.
35 minCHANCE! Bournemouth comes straight back at Burnley and a flick-on from Mousset finds the feet of Pugh, but his rising effort is well dealt with by Heaton in the Clarets goal. Is this game finally starting to warm up?
39 minSHOT! Daniels is the next player to try a speculative shot but it was always rising and heading over the crossbar. Just over five minutes to go until the break. Despite the lack of action, this first half has flown by.
43 minThere has been a goal at the Riverside Stadium and it isn't good news for either Bournemouth or Burnley. Jay Rodriguez has given Southampton the lead in the North-East.
44 minCHANCE! As that goal was going in at one end of the country, Boruc was making a terrific save at the opposite end. Arfield must think he is about to score when receiving the ball from eight yards out but the Polish stopper manages to get himself in the way.
3.48pmThe half-time whistle goes at the Vitality Stadium and Bournemouth lead thanks to that Stanislas's goal. Burnley have matched their hosts but for now, their former winger's strike is the difference between the two clubs.
4.01pmThe teams have made their way back out. We are almost ready to for the second half.
46 minBournemouth get us back underway. Burnley have introduced Andre Gray for Ashley Barnes.
48 minNot a lot to choose between the sides since the restart. The introduction of Gray naturally offers more of a threat in Burnley's attack, but that will also free up a bit more space for Bournemouth.
52 minCHANCE! Was that the moment for Mousset? Some excellent work from Pugh gives him the chance to cross for his young teammate but he flicks the chance wide of the post.
54 minSHOT! Steve Cook gets on the scoresheet every so often but not in these circumstances. The defender unleashed a ferocious effort from distance but it was straight at Heaton.
55 minSUBSTITUTION! Dyche has seen enough. Boyd is replaced by Robbie Brady.
56 minSHOT! Fair play to Burnley. They have absorbed pressure from their hosts and are now looking for an equaliser. Moments after Westwood fired wide from distance, Arfield went even closer with a shot which whistled past the post.
59 minIt could be game over at the Riverside. Southampton have taken a 2-0 goal lead against Middlesbrough, with Redmond adding to Rodriguez's earlier striker. As it stands, both Bournemouth and south coast rivals Southampton are moving level on points with eighth-place West Brom.
61 minCHANCE! Back come Bournemouth and Mousset has failed to convert another opportunity. King's cross found the striker at the back post, but his header was straight at Heaton.
63 minCHANCE! This is turning into the kind of game I predicted shortly before kickoff. After being found by Pugh, a sharp turn from King led to him getting a shot away on the edge of the penalty area but his curling effort went just off target.
65 minSUBSTITUTION! After receiving a knock, Mousset is being replaced by Ryan Fraser. Decent afternoon for the 21-year-old, but he could have done with a goal.
68 minSHOT! This is why he is attracting the attention of clubs higher in the Premier League table. King gets himself from the corner into a goalscoring position, but he sees his shot well blocked. He has impressed once again this afternoon.
72 minWhile Bournemouth have had the better of proceedings since the hour mark, Burnley remain a threat. Gray hasn't done much since being introduced at the break but the home side cannot afford to gift him - or Vokes - a chance in these closing stages.
75 minSUBSTITUTION! Final change for Burnley, but Johann Berg Gudmundsson coming on for Arfield.
79 minAs we enter the final 10 minutes, Burnley are throwing players forward in an attempt to find an equaliser that they probably think they deserve. Bournemouth aren't necessarily known for their clean sheets but they are digging in here.
82 minSUBSTITUTION! A second change for Bournemouth bees Dan Gosling take the place of Arter.
4.57pmThe full-time whistle goes at the Vitality Stadium and Bournemouth have claimed yet another brilliant victory in the Premier League. Goals from Stanislas and King has helped the Cherries move back into the top half of the table with one game remaining. It also ensures that they will finish above today's opponents Burnley.
4.57pmThat will be all from Sports Mole for this game. Thank you for joining us this afternoon and we hope to see you again soon. Goodbye for now.