Overnight leader Rob Stannard finished almost a minute down on the stage winner, but Hamilton was able to match Landa's attack with 15km to go of the final 22km circuit, and the two worked well together to finish 10 seconds ahead of the chasing bunch, which was led home by Riwal Readynez's Alexander Kamp.
"It's a shame for Lucas not to get the win, but we're very happy that we've increased our lead in the general classification, and we're in a pretty good position now going into stage three," said Mitchelton-Scott sports director Matt Wilson on the team's website, with Hamilton now leading his teammates Damien Howson and Nick Schultz, who are both 16 seconds down in second and third place, with Landa having moved up to fourth overall, another six seconds back.
"The stage today was a pretty solid day, and because we had the jersey [with Stannard], the team rode awesomely on the front all day and controlled the whole race," explained new leader Hamilton. "Everyone did an amazing job, which made it easy for us guys who were waiting for the final climb.
"We pretty much just made sure that we held on to the GC today," he continued. "Obviously a stage win would have been nice, but it was good to be able to cover all the moves, and we had a couple of options.
"We weren't too stressed about Movistar, as they lost time in the team time trial yesterday [stage 1b], but obviously Landa was the strongest climber today, so when he went, I went with him, hoping we could get a gap on the Team Sky guys, who weren't so far behind on the GC."
Sky – who finished second to Mitchelton-Scott on Wednesday's TTT – are now led in the GC by David de la Cruz in fifth place, 26 seconds behind Hamilton, with Herald Sun Tour winner Dylan van Baarle in the same time in sixth place.
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Friday's third stage takes place on a circuit around Forlì – 50km south-east of where the 2019 Giro d'Italia will start, in Bologna, on May 11 – and features seven climbs of the Rocca delle Caminate.
The five-day Coppi e Bartali finishes in Sassuolo on Sunday.
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