The world and European champions produced a typically efficient performance in chilly Minsk, dominating possession and quickly snuffing out any forward forays by the outclassed eastern Europeans.
The first meeting of the two sides was a useful warmup for Spain ahead of Tuesday's qualifier against France in Madrid when coach Vicente del Bosque's makeshift defence featuring converted midfielder Sergio Busquets will face a much stiffer test.
The game at Atletico Madrid's Calderon stadium could go a long way to deciding who wins the group.
"It was a good performance... the players felt very comfortable from the start and linked up well," Del Bosque told a news conference. "They played with depth, won the ball back well and the talent and quality of the players did the rest.
"We were superior and didn't let them play. They couldn't operate at their level due to our strengths and they did not feel at ease on the pitch."
After Cesc Fabregas and David Silva went close early on, full-back Alba opened the scoring in the 12th minute when he raced on to Pedro's flick, rounded goalkeeper Sergei Veremko and drove the ball into the net.
Friday's match was not shown on television in Spain as the country's cash-strapped broadcasters were not prepared to pay the price set by rights holder Sportfive.
