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."
Spain have six points from two games, level with France but with a superior goal difference to the team they knocked out in the quarter-finals of Euro 2012.
Georgia, who lost 1-0 to Spain in Tbilisi last month, are third on four points with Finland on one and Belarus on zero.
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.
Silva sent Pedro clear to make it 2-0 nine minutes later and the Barcelona forward added his second in the 69th when he sped away from the defence and lifted the ball over the onrushing Veremko.
Fabregas, playing in the roving forward position he occupied at Euro 2012, set up his club team-mate to complete his treble in the 72nd minute before substitute David Villa, another Barca man, crashed a shot against the crossbar.
Spain last failed to win a World Cup or European Championship qualifier in a 1-1 draw with Iceland in Reykjavik in September 2007 and have now won all 20 under Del Bosque.
They have gone a national record seven competitive games without conceding a goal - Italy were the last team to score against them in a 1-1 draw in the group stage at Euro 2012 in June.
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.
It was the first time a Spanish World Cup qualifier had not been shown on national TV, local media reported, and was the latest reminder of how the country is suffering from the economic crisis.
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