Victory at the Borisov Arena kept European champions Spain in second place in Group C with 15 points from six games -- three points behind group leaders Slovakia.
The 64-year-old Del Bosque, the first Spain manager to reach the century milestone, gave a start to 22-year-old Juventus forward Alvaro Morata, who scored his first goal for his country in March against Ukraine.
Despite being without the injured Andres Iniesta, the visitors immediately took control of the game.
Pedro Rodriguez had a good chance from close range after two minutes but hit the ball straight at goalkeeper Andrei Gorbunov.
Morata then fired a shot into the side netting from an acute angle after another Spanish attack.
Iker Casillas, who was winning his 162nd cap, was a virtual spectator as Belarus offered little in attack.
Spain eventually went ahead on the stroke of halftime.
Cesc Fabregas sent in a cross from the left flank towards the far post and Gorbunov was unable to cut the ball out and Silva's fine strike put the visitors in front.
Belarus offered more in the second half and Sergei Kornilenko had an excellent chance to equalise, but Casillas turned the ball behind with his leg.
Spain could have extended their lead as Santi Cazorla's 20 metre effort forced a fine save from Gorbunov at his near post, while Silva went close put was unable to beat the Belarus goalkeeper after being put through one on one.
(Reporting By Dmitriy Rogovitskiy)
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