The Mexican forward scored his 10th goal of the season to put his side ahead, but Levante tallied from the spot as well to force a 1-1 draw.
The prolific Vela, who remains reluctant to join El Tri during its World Cup qualifying campaign, hit a left-footed strike inside the right side of the goal to score in the 18th minute, putting Sociedad ahead after winning the penalty when Nikos Karabelas fouled him at the top of the area. Levante's Michel equalized from the spot 11 minutes later, though, and Sociedad could not find a winner despite being a man up for the final 33 minutes after Karabelas was sent off for his second yellow card in the 57th minute.
As a result, Sociedad lost a bit of ground in its quest for a Champions League berth, as it trails Malaga -- a 1-0 winner over Athletic Bilbao on Saturday -- by five points for fourth place in La Liga. Sociedad, Valencia and Rayo Vallecano are all level on 37 points, though the latter two sides have a game in hand.
The goal was Vela's fifth in his last 10 matches and tied him with Rayo Vallecano's Piti and Sevilla's Alvaro Negredo for seventh most in the Spanish top flight.
Other Mexican attacking stars Andres Guardado and Giovani Dos Santos were in action against one another Sunday as well, with Guardado's 10-man Valencia outlasting Dos Santos' Mallorca 2-0. Guardado did not factor in either goal.