Barcelona: Ex-Italy coach Cesare Prandelli got off to a winning start in La Liga as his new Valencia side triumphed 2-1 at Sporting Gijon on Sunday, while Villarreal maintained their impressive opening to the season by thrashing Celta Vigo 5-0.
Former Atletico Madrid and Watford midfielder Suarez provided the ideal launch pad for Prandelli with a thumping right-foot drive to score in the seventh minute.
Valencia were pegged back by Carlos Castro`s header just before halftime but retook the lead in the 65th minute when Suarez calmly turned a knockdown into the net.
The win took Prandelli`s team out of the relegation zone and up to 14th on nine points from eight games.
"What I liked most was the union, the desire to do things well and the spirit of wanting to work hard," Prandelli told a news conference.
"We played with a lot of intensity at a difficult ground against a very organised team and it was a very balanced game."
Unbeaten Villarreal raced into an eighth minute lead against Celta when Roberto Soriano nipped in behind the defence to latch on to a pass by Manu Trigueros and tuck the ball into the far corner.
The Italy international, a 14 million euros ($15.68 million) signing from Sampdoria in the close season, scored again four minutes later by capitalising on a stray pass from Celta goalkeeper Sergio Alvarez.
Villarreal`s Cedric Bakambu marked his first start of the season since returning from injury to hit the third in the 38th and an own goal by Daniel Wass extended their lead just after the break.
Celta were unrecognisable from the side that beat champions Barcelona 4-3 last week and their misery was compounded when Sergi Gomez was sent off for a second booking in the 87th and Trigueros completed the rout in added time.
"Celta are a direct rival and like us are in the Europa League so this is an important victory," said Villarreal coach Fran Escriba. "It was our most complete game so far this season."
Villarreal moved up to fifth place on 16 points, level with Barcelona in fourth, while Celta are 12th on 10. Atletico Madrid lead the table ahead of Real Madrid, with both sides having 18 points after easy wins on Saturday, followed by Sevilla with 17.
Earlier on Sunday, Athletic Bilbao rallied from a goal down at halftime to produce a stirring home fightback in the Basque derby as they beat old rivals Real Sociedad 3-2.
The visitors opened the scoring when David Zurutuza crashed in a volley following a corner in the 16th minute but Athletic responded superbly and a wonderful individual goal from Iker Muniain deservedly pulled them level in the 51st.
Within 10 minutes Aritz Aduriz had put Athletic in front with a cool chip over the stranded Rulli and then the veteran striker teed up Inaki Williams to knock in the third in the 72nd. Inigo Martinez netted a late consolation for Sociedad.
Athletic stay sixth with 15 points, while Sociedad have 10.
Alaves drew 1-1 at home to Malaga as a late thunderbolt from Roberto Rosales cancelled out Deyverson`s early goal in a feisty game that ended with each side having a player sent off.