Goals from Aaron Ramsey and Alexandre Lacazette gave the Gunners a 10th league home win on the bounce and moved them above bitter rivals Tottenham for the first time this season.
Just three points separate the Gunners, Spurs, Manchester United and Chelsea as the battle for the Champions League spots looks like going down to the wire.
Emery's men have timed their run of impressive form well heading into the final part of the season, but with five of their remaining seven games away from home, the Gunners boss is not expecting it to be easy.
"Our target is very clear," he said. "It's going to be very difficult but step-by-step we've started to rise up the table after the first two matches in the Premier League when we lost against Manchester City and Chelsea.
"We are improving and now we are third. But we know it is going to be difficult for us because our opposition is big opposition and it is going to be very tough for us.
"We need to convince people that we can be consistent away. The opposition is going to demand us to get a lot of points at the end of the season and I am only going to think of the next match.
"Our challenge is away because we are going to play five matches away in the last seven matches. Our challenge is to be as consistent away as we are at home."