Landa and Hamilton pulled away from the main contenders on the final finishing circuit of the short but hilly 140km stage from Riccione to Sogliano al Rubicone.
It was a strong return to form for the Basque climber after a dismal end to 2018, DNF'ing a series of races after finishing the 2018 Tour de France where he was lucky to finish seventh overall following a heavy crash on Stage 9.
In late January, Landa abandoned Challenge Mallorca due to injury and only returned to racing for Saturday's Milan-San Remo.
“I saw myself able to conduct such an action from the last climb and all the way to the finish, and I was calm and confident because I had a strong team by my side," the Spaniard said of his stage win. "With so many team-mates together who could also ‘block’ the race behind if the peloton approached at the descent.
"I knew I could make it and I only wanted the race situation to allow myself giving it a try. I’ve got through so many difficult injuries, including last January’s Mallorca crash and collarbone fracture, and I know it takes so long and requires so many efforts to make it back. This victory pays off all those efforts and gives me a lot of confidence. I know now I’m on the right path, and I can still do well in the Giro.
The leader's jersey didn't have to travel too far, Hamilton assuming the lead from Aussie team mate, Robert Stannard.
For Hamilton, it is his chance to shine after using his strong early season form to faithfully serve Daryl Impey as he claimed a record-breaking back to back Tour Down Under victory, and Nick Schultz's second place overall at the Herald Sun Tour, finishing sixth himself.
Schultz and Damian Howson sit just behind their team mate on GC after Mitchelton-Scott smashed the Stage 1b TTT. Landa lies fourth, 22 seconds from the lead.