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Genoa were struggling to keep possession of the ball and Lulic threatened again with a powerful low strike that was tipped round the post by Perin.
Midway through the half, Djordjevic connected with Antonio Candreva's cross from the right, but the Serbian could only direct his header over the bar.
Perin was proving hard to beat and he denied Lazio once more with a save from Anderson's drilled attempt.
The woodwork came to Genoa's rescue moments later as Djordjevic's header at the near post looped over the keeper and came back off the bar.
Just past the hour-mark, Lazio went close with another headed effort, but, after meeting Edson Braafheid's cross, Candreva couldn't direct his effort on target.
With five minutes of the match left to play, Stefan de Vrij was sent off for Lazio after picking up a second yellow card for handling the ball.
It took two minutes for Genoa to make their numerical advantage count as Pinilla met Diego Perotti's header back across the box to nod in from close range, and his side held on under late Lazio pressure to claim all three points.