Despite dominating the game for the majority of the four days, Chris Rogers’ side came up short as Yorkshire held on to their unbeaten start to the campaign - although the draw did see Warwickshire dislodge them at the top of the table.
The loss of 19 overs in the day to rain might just have been the difference as Yorkshire finished on 141-6 after being forced to follow-on - still 110 runs behind the hosts’ first-innings score of 562-7.
Resuming their first innings on 306 for nine, the White Rose were quickly bowled out for 311 when Jamie Overton bowled Steven Patterson for 32 to end a last-wicket stand of 74 with Jack Brooks.
Somerset, as expected, enforced the follow on and bowled particularly well with the new ball.
Adam Lyth and Alex Lees batted with due care and attention prior to lunch, but the afternoon session brought the bowlers some reward.
Lyth, who has scored over 800 runs at the County Ground in his last seven matches, was first to go - bowled by Overton when playing back to a short ball that kept low.
Will Rhodes was caught at short-leg by Tom Abell off the bowling of Jack Leach, and four runs later Lees, who had scored only 11 off 97 balls, was bowled by Overton when offering no shot.
The tea interval provided Yorkshire with some respite, but when Andrew Gale was caught by Leach off the bowling of Tim Groenewald to leave the score 69-4, Yorkshire were facing an anxious final two hours.
Overton bowled with purpose and his third wicket came when Gary Ballance carelessly flicked the 22-year-old to Leach at square-leg.
Groenewald picked up the wicket of Adil Rashid with 10 overs remaining and at that stage a victory for Somerset looked a distinct possibility, but Jack Leaning and Liam Plunkett held out in the final hour, finishing unbeaten on 29 and 20 respectively.
Fast bowler Overton was the pick of the Somerset attack with figures of 3-26.
Somerset: Trescothick, Abell, Rogers (captain), Hildreth, Allenby, Trego, Davies, Gregory, Groenewald, J Overton, Leach.
Yorkshire: Lyth, Lees, Rhodes, Ballance, Gale (captain), Leaning, Rashid, Hodd, Plunkett, Patterson, Brooks.