However, manager Juan Ignacio Martinez refuses to get carried away with his side's current position and says that, given the financial disparity between the teams, just keeping the run going for one more week against Malaga would be a huge achievement.
He said: "Hopefully we can keep this level going for one more week.
"We are playing a team I am not going to find out about tomorrow, due to the amount of money that have they were able to maintain their status last year and now the privilege to sign players of an excellent quality. We have other values, such as effort and determination."
That difference in resources is highlighted by the fact that Martinez will be forced into at least one change from the side that won at Real Betis two weeks ago as Xavi Torres' transfer from Malaga contained a clause that means Levante would have to pay should they field the midfielder against his former club.
Martinez indicated that his place would be taken by either Miguel Pallardo or Francisco Farinos.
Malaga will also just make the one change from last time out. Julio Baptista was injured in a friendly against Real Jaen during the international break so Salomon Rondon should claim his place up front alongside Ruud van Nistelrooy.
The Venezuelan striker was part of the side that beat Argentina 1-0 on Tuesday night and he is hoping to recreate that success as he goes in search of his first goal of the season on Sunday.
"It will be a very competitive match, but we're going there with the mentality that we need to pick up the three points," Rondon said.
"All strikers want to score goals and doing so is just a matter of time. At the moment we aren't quite in full flow going forward but generally we have started the season very well."