The Cherries were 2-0 up at the break following goals from Matt Ritchie (10) and Lewis Grabban (27).
Wednesday rallied briefly towards the end of the game and Jacques Maghoma pulled a goal back in the 82nd minute.
Grabban had a chance to add a third for Bournemouth in the final minute, but his shot was saved by Damian Martinez.
“I was delighted in the first half because I thought it was a very good display,” said Howe. “We counter-attacked with real quality and pace and Lewis Grabban led the line well, causing problems with his pace and mobility.
“We got the first goal, which we always thought was going to be all-important. The second half wasn’t pretty to watch for either manager but we dug in and got the win.
“We built on the Reading victory in terms of our performances without getting the results. You do need wins to back it up so today was very important.
“Losing ‘Cookie’ (Steve Cook) was a huge blow for us as he’s been excellent for us. He felt his hamstring on Tuesday but we believe it’s not too serious so we hope to get him back relatively shortly.
“Elliott Ward came in without a training session after five weeks out and he was excellent alongside captain Tommy Elphick, who led by example as well. They formed a very good partnership.
“Matt Ritchie is a huge player for us and we always felt he would be this season. He’s a huge goal threat, cutting onto his left foot. Every time the ball falls onto his left foot, you fancy him to score.
“Our priority now is a long overdue home win. Of late, we’ve failed to turn our dominant performances into victories.”
Sheffield Wednesday caretaker manager Stuart Gray said: “It was very disappointing. I thought we started quite well but then sloppy defending has cost us.
“Suddenly we’re chasing the game. It was a similar thing again with poor defending for the second goal.
“We’re short of strikers so in the end I had to put Reda (Johnson) down the middle. In the last 10 or 15 minutes, we got a goal back and we got into several good positions but our final ball let us down.”