Jacques Maghoma pulled a goal back for the hosts in the closing stages of the game, as they threatened to stage a late rally, but Bournemouth held on to claim all three points.
The result came as a blow to Wednesday caretaker manager Stuart Gray's hopes of staking a claim for the job on a permanent basis. It also means the Owls have still recorded only two home victories so far this season.
After Wednesday enjoyed some good early possession, without testing Lee Camp in the Bournemouth goal, the visitors opening the scoring in the 10th minute with their first effort.
Ritchie went unchallenged just outside the area and fired in a low shot which goalkeeper Damian Martinez got a hand to but failed to keep out.
Andrew Surman then tried a 20-yard effort and this time Martinez was equal to it, diving to his right to turn the ball wide.
As Bournemouth continued to press, Elliott Ward put a header wide.
Lewis Grabban put the Cherries further ahead after 27 minutes, receiving a fine ball from Harry Arter and racing into the area before cutting inside from the right and beating Martinez with a shot at the goalkeeper's near post.
Wednesday improved a little towards the end of the half with Jermaine Johnson having a shot saved by Camp. The Bournemouth goalkeeper also had to keep out an effort from Maghoma, turning his header wide.
The impressive Arter, who caught the eye with a composed performance in central midfield, fired in a free-kick which was saved by Martinez.
Wednesday defender Miguel Llera headed away as Grabban looked to get on the end of a cross from Ritchie.
Owls striker Atdhe Nuhiu tried to carry on after receiving lengthy treatment, but he was forced to go off a few minutes later.
A double substitution was made by Wednesday, with Jeremy Helan and Andelko Savic coming on in place of Nuhiu and Jose Semedo. The change appeared to spark a little life into Wednesday as they tried to force their way back into the game.
Wednesday were awarded a free-kick around 25 yards out, from which Llera fired in an effort which was only just over the bar.
Maghoma reduced the arrears with a shot from close range after a mix-up in the Bournemouth defence saw Charlie Daniels fail to clear.
Grabban had a chance to score his second goal of the game in the last minute after seizing on a weak header back from Llera but his angled shot was comfortably saved by Martinez.