Matt Ritchie forced a save from Asmir Begovic with a 30-yard effort and Steve Cook stopped a goal-bound header from Gayle.
Daniels' corner came courtesy fo Elliot palming a Jermain Defoe strike behind, and Cook nodded back across goal into the opposite corner to secure a vital win for his team. "He was strong, he pressed, he ran, he looked a goal threat and if he plays like that he'll get the goal total he got last season".
The hosts did have the ball in the back of the net in when Ritchie's terrific, bending effort struck the post and was followed in by Gayle, who was - perhaps harshly - ruled offside.
Cook's victor came as the visitors launched a late assault with Marc Pugh seeing a late effort blocked on to the post and substitute Jermain Defoe forcing a diving save from keeper Rob Elliot, although they had earlier survived a stern examination of their defensive solidity.
Begovic was kept busy as the game restarted after the interval - the Bosnian palming Joselu's header from a Jonjo Shelvey corner over the bar.
They were at it again moments as a long punt from Charlie Daniels managed to find King, despite protest for offside the Norwegian worldwide continued to push into the area but the tight angle worked against him when it came to final product as Elliot took into his body. "We were second best in the first half but we upped our game", Bournemouth boss Howe told BBC Sport. King's flick split the home defence and the striker raced onto the pass but fired a left-foot shot into the side-netting when one on one.
Jacob Murphy came on in a final change, but it was to be Bournemouth's afternoon.
However, while delighted with the resilience his side showed to snatch the points on Tyneside, Howe insists it is only a start.
It was inswinging corner from Andrew Surman and it was simple enough for The Cherries, as Cook rose highest and his bullet header past Elliot sent both the Bournemouth bench and away section into complete euphoria.
"But it's a great header from Steve Cook and a deserved three points I think".