The visitors batted first and had Rudolph lose his way after making 62 when he was caught by Tim Ambrose off the bowling of Rikki Clarke.
Michael Vaughan followed shortly after for sixteen when he was caught by Jim Troughton off the bowling of England Lion Chris Woakes.
Yorkshire closed on 258-2.
In the Test Match at Lords, Ravi Bopara finished 118 not out as England closed on 289-7. Matty Prior made 42, Cook, 35 and Broad 38.