Warwicks took their score to 403-8 before declaring. Lancashire batted all afternoon.
Tahir and Ant Botha both took four wickets apiece as Chilton top scored with 85 and du Plessis hit 79.
Boyd Rankine and Chris Woakes also took wickets to see Lancashire all out for 317 and the match declared a draw.
Tomorrow, Warwickshire take on Glamorgan in a Pro40 game at Edgbaston. Play is due to start at 13.45pm.
In the Ashes match, England skittled Australia all out for 215 and then were 311-6 at stumps. Matt Prior top scored with 61 runs as England finished the day 521 runs ahead.