Manager Vilanova, back at the helm after surgery on his parotid gland after contracting cancer for the second time, was given the easiest of nights as Barcelona coasted to a one-sided 4-0 win.
They had scored all of their goals by the half-hour and after that it was procession football, with Pedro twice denied a hat-trick by the offside flag while other chances also passed.
After Xavi had opened the scoring, Pedro then chimed in with his brace before Lionel Messi added a penalty.
The win leaves Barcelona 11 points clear at the summit after nearest challengers Atletico Madrid could only draw 1-1 at Real Mallorca.
Raul Garcia broke the deadlock in the 72nd minute for an Atletico side shorn of star striker Radamel Falcao due to suspension, and Mallorca punished the visitors’ inability to see them off as Kevin Garcia popped up with an equaliser three minutes from time.
Karim Benzema had swept the champions into the lead after 90 seconds but Jose Mourinho’s decision to once again leave goalkeeper Iker Casillas on the bench backfired six minutes in as replacement Antonio Adan brought down Carlos Vela inside the area and was sent off.
Xabi Prieto slotted home the penalty, and both sides exchanged further goals before half-time as Sami Khedira put Madrid back in front only for Prieto to level five minutes later.
Cristiano Ronaldo looked to have sealed the points with two goals in two minutes midway through the second half, but Sociedad were given another lifeline when Prieto completed his hat-trick with 15 minutes remaining.
The visitors themselves were reduced to 10 men on 80 minutes as Dani Estrada was shown a second yellow card for bringing down Ronaldo and the Basques failed to muster another effort on goal.
In the day’s early kick-off, two goals from Iago Aspas and a wonderful strike from Alex Lopez were enough to hand Celta Vigo a 3-1 win over Valladolid.
Aspas enhanced his burgeoning reputation with a fine run and finish after eight minutes, but Valladolid were level moments later when Alberto Bueno converted from the spot after Javi Varas had brought down Javi Guerra.
Aspas restored the lead with a penalty of his own on the half-hour and Lopez sealed the points seven minutes into the second half with a brilliant strike from 25 yards.