Sussex resumed on 276-4 and batted constantly. Luke Wright made 71 with Carl Hopkinson hitting 119 from 193 balls before he was caught by Botha off the bowling of Jon Trott.
Hodd made 59 before Sussex declared on 429-8.
Warwicks then went into bat and although Westwood and Tony Frost went cheaply, Ian Bell made 55 before a draw was declared with Warwicks on 97-2.
Warwickshire's next game is a Pro40 match against Middlesex at Edgbaston on Tuesday. Play is due to start at 4.40pm and you can hear commentary on BBC Coventry & Warwickshire.
In the Ashes match, Australia closed on 479-5. Katich was out for 122 with Ponting 150 and Clarke 83.