On day three, Warwicks added 58 more runs to their over night total before the final wicket which saw Tahir caught and bowled by Rayner, leaving Chris Woakes 49 not out fell.
With Warwicks all out for 407, Sussex went into bat and made 55 before the first wicket was taken by Tahir who also added the scalps of Yardy (57) and Goodwin (22).
In between that, Ant Botha had Joyce caught for 29. At the close, Hopkinson was 64 not out and Luke Wright 59 as the visitors finished the day on 276-4.
In the Ashes match at Cardiff, Australian were 249-1 in reply to England's total of 435 all out.
At Stumps, Simon Katich was 104 not out and Ricky Ponting 100 not out.