Zito (1-0) allowed three hits and walked three in the home opener for San Francisco. Prior to the game, the Giants raised their second World Series championship banner in three seasons.
In their last three visits to San Francisco, the Cardinals have produced one run. The previous two contests were the sixth and seventh games of the NLCS last October.
Sergio Romo came on in the ninth to finish off the shutout and pick up his third save.
Pagan then walked on four pitches.
San Francisco has won 15 games in a row when Zito has started dating to last August.