The Argentine goalkeeper Roberto Bonano, released by Barcelona two years ago, produced a succession of first-class saves to earn Alaves a point on their return to La Liga.
Barcelona laid siege to the Alaves area, but last season's leading scorer, Samuel Eto'o, winger Ludovic Giuly and the world player of the year, Ronaldinho, were unable to find a way past Bonano.
"It was a good game against a well-organised team," said the Barcelona captain, Carles Puyol. "We tried everything we could but when 'Tito' [Bonano] didn't stop us we ended up being frustrated by the woodwork."
Valencia, Barcelona's predecessors as champions, made amends for their midweek defeat by Hamburg SV in the Intertoto Cup when Pablo Aimar secured a 1-0 win at home to Real Betis.
The Argentine playmaker curled in a right-foot shot after neat control on the fringe of the area eight minutes into the second half.
However, the honour of scoring the first goal of the new season fell to Athletic Bilbao's midfielder Fran Yeste, who grabbed his side's opener in the 47th minute of their 3-0 home victory over their Basque rivals Real Sociedad.
He darted on to a deft through ball from Joseba Etxeberria and fired an angled shot past keeper Asier Riesgo two minutes into the second half.
Towering striker Fernando Llorente added the second four minutes later with a deflected shot. He broke down the right before his firm shot ballooned off the foot of midfielder Gaizka Garitano and into the net.
Bilbao's defender Luis Prieto wrapped up the points when he ghosted in at the far post to convert a free-kick taken by Tiko.
In Alaves, returning to the top flight after two seasons in the Second Division, the home side signalled their intentions from the start as they tried to muscle the visitors off the ball and play on the break.
Barcelona gradually found their rhythm and settled into their customary fluid passing game after the first quarter of an hour.
But Bonano produced reflex saves to deny Eto'o and Giuly before pulling off an acrobatic one-handed effort to turn a powerful drive from Deco round the post.
Frank Rijkaard's side continued their siege of the Alaves area in the second half but again came up against Bonano.
The Argentine parried a venomous drive from Ronaldinho and produced another spectacular diving save to stop his follow-up. Four minutes later he got the faintest of touches to turn another fierce shot from the Brazilian on to the post and then stood up well to stop Eto'o cashing in on a poor back-pass.
Barcelona remained camped in the Alaves half but were unable to find a way past Bonano. Eto'o lashed wide 17 minutes from time and then drilled an angled shot against the base of the post in the next attack, while Ronaldinho brushed the bar with two dipping free-kicks.
Alaves almost snatched an unlikely victory when striker Rodolfo Bodipo smashed a close-range shot against the woodwork after a lightning counter-attack.
Last season's runners-up Real Madrid began their bid for a first title in three seasons by visiting promoted Cadiz yesterday. Jonathan Woodgate was a surprise inclusion in Real's 20-man squad for their opening fixture. The 25-year-old England defender, who had been stricken by a thigh injury for the past 16 months, was included for a competitive fixture for the first time since his £13.4m move from Newcastle a year ago.
Woodgate told the Spanish newspaper Marca: "I still haven't done anything yet. I have to keep on working so I can play the full 90 minutes and to help the team achieve its objectives."
Woodgate came through a series of practice games in the past 10 days, prompting the Real Madrid coach Wanderley Luxemburgo to include him in the squad.