Cook’s first goal since 4 December 2016, a header from Andrew Surman’s corner, lifted the visitors three places up the table to 16th.
A match low on quality was heading for a goalless conclusion after both teams wasted good chances to score before Cook struck to earn the Cherries a second successive away win.
“It’s big psychologically for everybody connected with the club,” said Howe.
“Being in the bottom three is psychologically difficult.
“These days in the media, it’s rammed down your throat, to a degree, so to lift ourselves out of this position temporarily is a good thing, but now we have got to try to build on it.
“It sets us up nicely, being out of the bottom three before the international break.
“It’s all about the next game and trying to build on this win. Hopefully it’s a key turning point in our season.”
