The Tigers make the trip to the Emirates Stadium on Saturday with just two wins from their opening seven games of the season.
While admitting that it will be tough for Hull, Harper believes that Steve Bruce's side are capable of coming away from North London with a positive result.
"You have to be defensively tight when you go down to a place like Arsenal and you need to be on top of your game because they will ask serious questions of you," the veteran shot-stopper told the club's official website.
"We'll have to go down there and remain compact and be hard to break down and frustrate them as we have shown before that we can upset these sides."
Hull are currently in 11th place in the Premier League table.