Sam Vokes cancelled out a first half goal from former Claret Junior Stanislas, but Josh King snatched a victor seconds after the one-time Bournemouth striker netted his fourth in as many games.
Terry won his final Premier League title with Chelsea last night as the Blues beat West Brom 1-0 to put themselves mathematically out of sight with two games to spare.
Burnley responded well, and Scott Arfield should have perhaps done better with a wayward strike from the edge of the area before, at the other end, Marc Pugh fired straight at Heaton despite having King in plenty of space to his left.
Burnley fans thought that was the goal to rubber-stamp Premier League safety, but King had the final say moments later.
- Josh King's goals have been worth 12 points to Bournemouth this season - only Diego Costa's (15) and Sergio Aguero's (13) have been more valuable to their club.
"This is my first season where I have scored like this".
I'm very level-headed, I believe in the players so much, I believe we're capable of great things but we still have to prove that and if we were to drop our standards by a small percentage then it would be very hard.
Andre Gray is said to be frustrated by Dyche's preference of Ashley Barnes and Sam Vokes up front that has seen him relegated to the bench for three of the last four games.
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Asked if Bournemouth will struggle to keep hold of King, manager Eddie Howe said: "I don't think so".
"But you are right in one sense".
"Then, hopefully, we can go into next season and improve again".
"I want to play in that game, play well and get a result".
"To hit that 40-point mark last weekend was a massive achievement".
Burnley boss Sean Dyche has admitted that his stand-in defenders still have learning to do following a "really poor" second-half display against Bournemouth.
"We scored a late goal, could have nicked something, but the two goals we conceded - particularly the second - were really poor".
"I'm disappointed in the end, but over the season it's hard to question this group".