The Group H win means Andre Villas-Boas' side have a maximum six points from their first two games, their best start in the competition.
Artem Dzyuba gave the hosts the lead after 35 minutes from a Hulk cross but the Belgian side drew level 10 minutes into the second half with a Thomas Matton volley before the Brazilian laid on the winner for Shatov in the 67th.
Zenit found the going difficult against an organised Ghent side, who were more than comfortable on the ball in the opening stages.
Dzyuba had the first opportunity of the game but sent the ball wide from close range after good work on the right flank from Igor Smolnikov, but he soon made amends.
A searching pass from captain Danny put Hulk through on the left. The Brazilian showed the strength his name suggests to hold off the challenge of Rafinha, before standing up an inch perfect cross which was met by a towering header from the Russian international, powering the ball past Matz Sels.
The goal shocked Ghent, but the Belgian side showed fine resolve to draw level.
Captain Sven Kums clipped the ball towards the far post and the in-form Matton sent a fine right-footed volley past the despairing dive of Mikhail Kerzhakov, to net his fourth goal in three games.
The goal sparked Zenit into life, and they were roared on by a partisan home crowd at the Petrovsky Stadium.
Hulk was once again in the thick of things as his second assist helped restore the reigning Russian champions' lead in the 67th minute.
The Brazilian's fine pass put Shatov through on the left of the area and the 25-year-old had time to take a touch before lifting the ball over Sels to make it 2-1.
Zenit easily held on for victory and their next match is at home against Olympique Lyonnais, while Ghent travel to Valencia.
(Editing by Rex Gowar)
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