Having bowled the hosts out for 314 after Stephen Peters had won the toss, the visitors closed on 39-0 which leaves them 275 runs in arrears.
Despite the fact that relegation to the second tier is almost a certainty, the County continued their improved form in the four-day game in the south west.
David Willey was the pick of the attack with 4-64 and he was well supported by Muhammad Azharullah who weighed in with 3-67.
Only Neil Wagner went wicketless with the New Zealander’s 21 relatively expensive overs going unrewarded.
For the hosts, Alex Barrow top scored with a 97-ball 88 and Nick Compton contributed a more circumspect 79 as a recovery of sorts was staged from a potentially perilous position of 70-4.
With 11 overs to negotiate before stumps, Peters and James Kettleborough ended the day on 14 and 18 respectively and the aim on day two will be to secure a first innings advantage.