The victory at Vitality Stadium was the Cherries' third win in a row and now pushes them into 13th place in the Barclays Premier League table.
Yet Howe still believes his side are not yet certain of safety.
"It was a good game for the neutral today," Howe said.
"It was played at a frantic pace, an end-to-end game which wasn't good for either party involved!
"But it was another big win for us, Swansea are a good side who play the game the right way and are well managed. They've had a disruptive couple of weeks but they showed good character not only to bounce back from that but to going behind twice.
"We showed great character ourselves though to bounce back from those setbacks and find another gear.
"I'm not going to say 'yes, we're safe,' nothing has been decided today. There is still more to do and we have some tough fixtures coming up."
The victory over the Swans saw Joshua King notch his second in as many games, and also saw Max Gradel score his first goal since his return from a six-month injury lay-off.
The Cherries boss was full of praise for both players.
"I'm so pleased for Max," Howe continued.
"The way he came back shows he's made of special stuff. I wasn't expecting Max to run to me either!
"He's plays with a smile on his face and it's been a difficult season for him. He's showed great determination and it's great for him to come back and adapt so quickly.
"Joshua was terrific as well. He's a good lad with terrific temperament, he's worked hard and been patient to get the goals his performances have deserved."