Midfielder Aaron Ramsey feels Arsenal are growing in self-belief with every big win.
The Barclays Premier League leaders continued where they had left off against Liverpool by producing a smash-and-grab raid on the Germans' Westfalenstadion fortress, where an 11th goal of the campaign for Ramsey just after the hour proved enough to take all three points back to England and put Arsene Wenger's men back on course for qualification from Group F.
Arsenal have won eight of their opening 10 Premier League matches, having been undone at home by Aston Villa on the opening day, but last week crashed out of the Capital One Cup against a second-string Chelsea side.
Pundits have been split over whether the Gunners, lifted by the club-record singing of Mesut Ozil, can last the distance.
Ramsey, though, believes Arsenal can only focus on delivering the required performance to keep themselves clear of the chasing pack.
"It was no easy task to come here and get the win. We will take an enormous amount of confidence from that and hopefully that will put us in a good position now to kick on and have a really successful season," the Wales midfielder said.
Asked if the Gunners have anything to fear from playing at United, Ramsey insisted: "Absolutely not. They have had a bit of a rough start, but they have overcome that now I think.
"They have had a few good results in the league and will be getting their confidence back up, but we are really confident ourselves.
"Our away record has been really good so hopefully we can continue building on that."
Ramsey added: "We had a fantastic run-in to last season and after the disappointing opening game of the season, we have managed to build on that and keep it going.
"Hopefully we can do that up until Christmas and then we know we have the ability to compete."
Arsenal goalkeeper Wojciech Szczesny made some crucial saves to keep Dortmund at bay, denying countryman Jakub Blaszczykowski at the start of the second half.
The Poland stopper sees no reason why the Gunners should not be confident of another top display at Old Trafford on Sunday.
"We are looking forward to Sunday now and we will be trying to make it a perfect week for us," Szczesny said on Arsenal Player.
"We have got two clean sheets and two results against quality opposition, one away from home at one of the toughest venues in Europe.
"It would be amazing to get nine points from these three games, when probably not a lot of people expected us to do.
"There is not a better time for us to go to Old Trafford.
"We are very confident and enjoying our football, so we are looking forward to it."
Ramsey may have grabbed the headlines after scoring another goal in an impressive individual campaign when he nodded in a knockdown from Olivier Giroud, but it was also another solid all-round defensive performance by the Gunners, with German centre-half Per Mertesacker the stand-out performer.
Szczesny added: "The key to what we have done in recent weeks has been the defensive performances of the back four and the whole team.
"They have been incredible and have all made my job very easy.
"Hopefully we can keep it going."
Arsenal were without England midfielder Jack Wilshere in Germany, and he will have a test on an ankle injury ahead of the United match, with a decision also impacting on whether he will be available for the upcoming international friendlies.
Midfielder Mathieu Flamini could return at Old Trafford having been sidelined by a groin problem since the Crystal Palace match.