The 20-year-old netted the precious winner on 87 minutes after being sent in battle in the second half.
Pape Diakhate tried to prevent the Danish player in the Dynamo box, but the latter managed to shrug off the tackle and slot home.
Having won the showdown, the London-based side secured the top spot in Group G with 11 points.
During the match, Arsenal up-and-coming striker Carlos Vela, who made his first Champions League start, exerted effective efforts in the early minutes.
Robin Van Persie failed to score from two free-kicks, all-in-all the hosts squandered so many opportunities within the match.
Eventually, Bendtner found his way to the net to send his side to the next round.
Meanwhile, FC Porto snatched a hard-fought 2-1 away victory over Fenerbahce to make it to the knock-out stage.
Lisandro Lopez scored a brace (19, 28), while Kazim Kazim pulled one back on 63 minutes.