Daryl Mitchell and Stephen Moore gave Worcestershire a good start with an opening partnership of 50 before seamer Danny Evans removed Moore for 21.
Evans then had Vikram Solanki (17) caught behind by wicketkeeper Ben Scott, while Tim Murtagh had Mitchell trapped lbw for 31.
Murtagh accounted for the dangerous Graeme Hick (15), but Smith continued to build a patient innings, reaching his half-century from 83 balls with successive boundaries off Evans.
The Worcestershire skipper was ably assisted by Steven Davies (22) and Batty, but the latter's promising innings was cut short when he was run out after a mix-up.
Tail-enders Matt Mason (25) and Andrew added valuable runs to steer their side to 349-9 before Mason was adjudged lbw to Indian left-arm spinner Murali Karthik just before stumps.