Bottas beat the Briton by 0.056 seconds in the afternoon, when Hamilton's title rival Sebastian Vettel of Ferrari was just 0.14secs off the pace.
Hamilton led Bottas by 0.435secs in the morning, with Vettel a second slower.
Ferrari's Kimi Raikkonen was fourth, ahead of Red Bull drivers Max Verstappen and Daniel Ricciardo.
Italian Grand Prix second practice results
Italian Grand Prix coverage details
Dutchman Verstappen and Australian Ricciardo face starting from the back of the grid because of a series of penalties for using too many engine parts.
McLaren's Fernando Alonso will join them for the same reason.
Hamilton has identified this race as a must-win, aiming to go into the Asian long-haul races with an advantage in the expectation that Ferrari will be difficult to beat in the next grand prix in Singapore.
"It's been a good day, a clean day," said Hamilton.