Both goals came from penalties in the first half, scored by Carlos Vela for the hosts and Michel for the visitors, who played most of the second half with 10 men after left-back Nikos Karabelas was sent off for picking up two bookings.
Levante coach Juan Ignacio Martinez made seven changes from the side that beat Olympiacos 3-0 on Thursday but his players were more than equipped to cope with their opponents.
Real Sociedad dominated possession and took the initiative in attack but Levante, bolstered by the return of captain and colossal centre-back Sergio Ballesteros, managed to deal with them comfortably.
The hosts were awarded a penalty on 17 minutes when Vela was brought down just inside the area by Karabelas, who was booked for the foul.
The Mexican striker stepped up to take the penalty and sent Keylor Navas the wrong way to score his 10th goal of the season.
Ten minutes later Levante were given a penalty of their own, when right-back Christian Lell was pushed over in the box by Chory Castro, and Michel converted from the spot.
Levante were grateful to their goalkeeper Navas for keeping the score level before the break.
First he fisted away a shot by Vela and then he kept out a long-range effort by Antoine Griezmann. The French forward had another chance right before half-time, but could only head over the bar.
Raul Bravo made an excellent save from Michel shortly after the break, tipping his powerful, long-range shot on to the bar, and then kept out an effort from Pape Diop.
Karabelas received his second yellow card of the game on 56 minutes, which made it the eighth game in a row in which Real Sociedad's opponents had had a man sent off.
However, the Basques were unable to capitalise on their advantage against a sturdy Levante which gave them little room to create proper goalscoring chances.