Everton stunned Manchester United 1-0 thanks to a bullet header in the second half by Marouane Fellaini when both teams got their Premier League campaigns underway on Monday.

The visitors then introduced new signing and league player of the season Robin van Persie, bought from rivals Arsenal last week, for his debut but to no avail.

Lionel Messi's double and a David Villa goal on his return form injury helped Barcelona hammer visitors Real Sociedad 5-1 to give new coach Tito Vilanova the perfect start to their La Liga campaign on Sunday.

"It's always important to start with a win," Vilanova, who has stepped up from assistant to replace Pep Guardiola, said.

Earlier, Real Madrid were held 1-1 at home by a feisty Valencia side. Gonzalo Higuain gave Real a 10th-minute lead from Angel Di Maria's cross and, in stifling temperatures, they comfortably held Valencia at bay until just before the break.

"I expected more from my team," Mourinho said. "We haven't played a great game, but we did enough to win."

Up on the north coast, Real Betis overcame Athletic Bilbao at San Mames in an eight-goal thriller.

In the late game, Europa League winners Atletico Madrid came back to draw 1-1 at Levante with a spectacular long-range shot from Turkey midfilder Arda Turan in the 22nd minute.

Samir Nasri struck an 80th minute winner as Manchester City came from behind to begin the defence of their Premier League title with a patchy 3-2 win over promoted Southampton on Sunday.

New Chelsea winger Eden Hazard earlier lived up to all the hype inside the first seven minutes of his league debut by setting up both goals in a 2-0 win at Wigan Athletic.