Yorkshire resumed on 258-2 and Joe Sayers was able to take his total onto 173 before he lost his wicket to Patel and ended a third wicket partnership of 336.
Anthony McGrath was in fine form, hitting three sixes and 24 fours in an innings of 211 from 324 balls. He finally became one of four victim for Neil Carter who ended with figures of 4-129.
McGrath's dismissal left the score on 514-5 and when the six hundred came up in the 167th over, skipper Michael Vaughan declared with his side having two wickets in hand.
In reply, Warwicks were 81-1 with Coventrian Ian Bell not out on 33.
In the Test Match at Lords, Ravi Bopara was out for 143 and England were all out for 377.
Durham's Graham Onion's got stuck into the West Indies. He took 5-38 from 9.3 overs as the visitors went from 70-2 to 152 all out.
West Indies were ordered to follow on and when bad light ended the day early, were 39-2.