A century partnership for the sixth wicket between Craig Kieswetter and Johann Myburgh took Somerset into seemingly safe waters after two sessions of day three at Taunton.
The duo shared 112 to take the hosts, replying to 450, from 252-5 to 364-5 in the latter stages of the afternoon before former England one-day wicketkeeper Kieswetter fell for 63.
Kane Williamson had him caught at slip by Adam Lyth to claim his second wicket of the innings, the only Yorkshire success of the afternoon.
Somerset reached tea on 394-6 from 121 overs, with Myburgh 65 not out and Lewis Gregory unbeaten on 22, including a six.
The afternoon had started with five successive maidens shared by Steve Patterson and Ryan Sidebottom before Kieswetter and Myburgh ensured their side advanced from 277-5 beyond 301, thus avoiding the follow-on.
Kieswetter hit two sixes during the session off Jack Brooks and Adil Rashid on the way to a 111-ball half-century. Myburgh brought up his off 80 balls.