Leigh pulled one try back moments later through Adam Higson who dived over the line, before Gregg McNally raced over almost immediately after to make it 10-10 at half time, as Ryan Brierley converted his side's second try to level the scores going into the break.
Williams scored his second try early in the second period, with Addy converting again before adding a penalty.
Blythe then raced over to increase the Bulls' lead to 26-10 before Bob Beswick gave Leigh some late hope, touching down with five minutes left in the tie.
Brierley again converted, before Bradford intercepted a wayward Leigh pass to set Blythe away, the second-row racing 50 metres to touch over and put the game beyond the Centurions.
Addy, who had sent another penalty between the posts before Beswick touched down, secured the Bulls' victory by stroking over another conversion after Blythe's second try.