Newcastle dominated the first half, but didn't take their chances.
Callum Wilson missed a great one on one and Marc Pugh hit the post late on, before Cook's thumping header stole the points for the visitors to lift the Cherries out of the relegation zone ahead of the global break.
"It's a huge win", Howe told reporters afterwards.
"We did, and how we didn't seal the game earlier was like us this season, we haven't been clinical enough and you felt it could be another day like that".
- This is only the second time that Bournemouth have won back-to-back away games in the Premier League, with the previous occurrence happening in December 2015.
At such moments, with your side in the bottom three, there is not a manager in the game who would not be forgiven for losing it. Howe turned and looked to the sky.
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Wilson - starting a Premier League match for the first time since January - then saw a looping header well saved by a back-tracking Rob Elliot, before the goalkeeper was again called upon to parry King's half-volley.
Having withstood the early barrage, Bournemouth grew into the match and Josh King dragged wide from the edge of the area.
He added: "Callum Wilson was excellent, you miss chances, it happens. 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".
"You reflect on the recent games and the points we could have had - even against Chelsea we could have drawn and come out of the game in high spirits". We gave them the chance to believe they could score.
"We are much better than people were expecting".
"Maybe the break is good, we can keep working with the players".
"It's ideal, it sets us up nicely for the games to come".