The Gunners skipper scored in the 49th and 86th minutes of the Emirates Stadium clash which was enough to put the North Londoners through to the Round of 16 for the 12th straight season despite a late strike from Shinji Kagawa. The goals were van Persie's 16th and 17th in his 18th appearance in all competitions this season.
For the most part it was a hard-fought contest with Dortmund constantly trying to press the home side and make it hard for them to play but the class of Arsene Wenger's men shone through as they made it nine games unbeaten in all competitions and five undefeated in the Champion League.
Despite being unbeaten in seven matches prior to this, Dortmund could not get the result they were after and will now have to beat Marseille on match-day six and hope Olympiakos defeat Arsenal to qualify.
Arsenal had very little joy up front for most of the first half but managed to get the opening goal four minutes into the second through who else but van Persie who headed home for his second goal against Dortmund this season. Alex Song made an absolutely brilliant run down the left, dodging and weaving his way past three defenders before putting a cross in for his skipper who got the ball over the line despite the best efforts of Roman Weidenfeller.
Dortmund huffed and puffed after the Gunners took the lead but they found themselves two behind late in the game when van Persie hammered home his second from close range when Mikel Arteta's corner was glanced on by Thomas Vermaelen to the back post where the waiting Dutchman obliged with the goal that was to send the North Londoners through to the next phase.
Dortmund gave themselves some slight hope when Kagawa slotted home in injury time after an Arsenal defensive error but the damage had been done as the Gunners' slow start to the season keeps getting better and better.
TRIBAL ASKS: Is the early-season Arsenal crisis long gone? Do they have more resolve now?