Welbeck headed Arsenal in front after six minutes after meeting Sead Kolasinac's cross at Emirates Stadium.
Welbeck rounded off the scoring in the 50th minute as Arsenal put their drubbing at Anfield against Liverpool last weekend behind them.
Wenger insisted he plans to field a strong team against their German opposition despite the prospect of a trip to Chelsea on Super Sunday, live on Sky Sports Premier League.
Striker Harry Kane scored his 100th goal for Tottenham Hotspur, and his first two goals of the campaign, as the north London side beat Everton 3-0 at Goodison Park.
The Gunners came into the game on the back of two costly defeats by Stoke and Liverpool, but made the ideal start when Welbeck headed them in front after six minutes.
"If he can add the finishing, he's a team player as well, he is loved by his partners, so that's a lot of positives". Christian Eriksen doubled their lead close to half-time to confirm what would be a hard afternoon for the Toffees.
Everton's day was made worse nearly immediately after the restart, Kane doubling his tally to guarantee the points.
His first involved some fortune as Sead Kolasinac's cross came off his shoulder, but the second was a ideal finish into the far corner from a tight angle.
While Bournemouth was slightly fortunate to escape a penalty award as Adam Smith handled Ozil's volley, the visitors regrouped at the break and initially threatened as Jermain Defoe crashed a header against the post.
James Morrison set up a tense final 10 minutes by firing home, but the home defence stood firm to claim a precious three points.
"I had a chat with him after the game, he didn't look unhappy".
"Some teams who are the new favourites, they are not in a better position than us". Our two away games...
Southampton failed to register a shot of any kind in the first half and duly fell behind when Doucoure crashed in his second of the season shortly before half-time.
Lacazette fired home a handsome strike from the edge of the box.