The Team Sky man, 29, pulled away from the other riders in the leading group with 40 kilometres to go.
Stannard finished almost two minutes clear of Graham Briggs of JLT-Condor and ONE Pro Cycling's Kristian House.
The stage had been expected to end in a bunched sprint, but the main peloton, which included Mark Cavendish, finished more than six minutes behind.
Belgium's Julien Vermote, the winner of Monday's second stage, retained the overall lead.
Stannard, who got into a small breakaway soon after the start, said: "I train on these roads every day, since I was 18, so I really enjoyed it today and was giving it some down the descents.
"Cheshire East pulled out all the stops and got an amazing crowd out. Every town, every hill, there was massive crowds, it was great to see."
