The league leaders took the lead against the run of play, but had no answer to a determined second half showing from the Cherries.
A Ben Gibson own goal, as well as fine finishes from Harry Arter and Simon Francis ensured all three points for the home side.
“We showed belief throughout the game,” Howe told afcb.co.uk. “The crowd showed belief too even at a goal down. The supporters showed last week against Leyton Orient that they had a huge bearing on the game, and today they were fantastic again. They gave the players a lift, especially after the break and we scored at a good time. It was a really enjoyable second half.
“It was a special day for me personally and that was because of the reaction of the crowd. I have said time and time again, the supporters have always been fantastic to me. People might say it was about me, but it was down to the players. They are the ones who should take all the credit because they are the ones who did it on the pitch.
“In the second half, they showed great character against a side unbeaten in the league this season. It was a good achievement and there were some really good signs. The players have been a real pleasure to work with this week and I’ve really enjoyed it, and it’s great that we topped it off with a win.
Howe added that he was delighted to mark the start of his second spell in charge with a home win.
“In all honesty, it didn't feel like I’ve been away. It felt normal," he said. "When I walked out, it just felt like being at home again. I’m not saying that in a corny way, it was just a really good feeling. I was obviously hoping we would get the result and thankfully we did.”