Jose Mourinho's side claimed a thrilling 3-1 victory at the Emirates Stadium on Saturday to put the pressure on leaders Manchester City and move seven points clear of the fourth-placed Gunners.
United raced into a two-goal lead after 11 minutes, with Antonio Valencia and Jesse Lingard scoring after the visitors pressured Arsenal defenders Laurent Koscielny and Shkodran Mustafi into mistakes.
Arsenal dominated the rest of the match but were undone by another counter-attack that was finished by Lingard, having got themselves back into the game through Alexandre Lacazette.
United survived Paul Pogba's red card in the closing stages to see out a second win this week, following their 4-2 triumph against Watford, and Smalling felt the decision to start with Romelu Lukaku and Anthony Martial in attack, just ahead of Lingard, proved to be the key.
"I think we were carrying on from Watford and the fact that, when we play, obviously in this system, we can play with two strikers," he told MUTV.
"Quite often, they [Arsenal] are only used to playing against one. We put two up front and put them under more pressure and they are not used to that.
"I think that was one to enjoy, for fans watching the game and for us as players. It was end to end, but for us to get those two early goals, I think, meant Arsenal had to come at us and that's what made it a very entertaining game."
Smalling praised the way United defended their lead as a unit, especially after Pogba was dismissed for a foul on Hector Bellerin in the 74th minute.
"I think that's down to our tactical work and us being able to be strong," he said. "They probably had about four strikers on the pitch so it was a case of digging in and making sure, even the attacking players, were doing their job and everyone to a man was brilliant.
"I think Watford were going into our game on Tuesday on a great run of form and Arsenal, I don't think they've lost at home like we haven't, so I don't think we could have asked for anything more. It's been a great week."