Home striker Alexander Kerzhakov, just back from a thigh injury, almost scored after 10 minutes when he hit the post from eight metres following good work by fellow Russian international Roman Shirokov.
Rostov, who lost seven of their previous eight matches against Zenit, then went ahead after 18 minutes when the league's joint top scorer Artem Dzyuba beat the offside trap to cleverly set up Vitaly Dyakov and he made no mistake from close range.
The visitors went 2-0 up six minutes before the interval when Croat Hrvoje Milic laid on midfielder Timofey Kalachev's third goal of the season.
Spalletti made two changes at halftime, Viktor Faizulin and Oleg Shatov replacing the ineffective Andrei Arshavin and Konstantin Zyryanov, but Zenit still looked bereft of ideas while their forwards struggled against Rostov's well-organised defence.
Zenit have 36 points from 17 matches, three ahead of Lokomotiv Moscow and Spartak Moscow. Rostov are eighth on 23 points.
Spartak visit fourth-placed CSKA Moscow on Saturday and Lokomotiv take on Dynamo Moscow, who are fifth, in another derby on Sunday.
Zenit are second in Champions League Group G with five points from four matches, seven behind Atletico.
Porto are third with four points and Austria Vienna are rock bottom on one.
(Writing by Angel Krasimirov, editing by Tony Jimenez)
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