Shakib Al Hasan took four wickets on Surrey debut while Tom Banton hit his third first class century for the hosts.
The battle of the top two in the table began with the home side winning the toss and electing to bat first on a pitch expected to offer increasing turn as the match progresses. Banton hit a brilliant 132, one short of his career-best, with 16 fours and a six, while Tom Abell contributed 49 and James Rew 38.
But Surrey launched a determined fightback with the second new ball to limit the damage from 305 for five at one stage.
Bangladesh left-arm spinner Shakib Ul Hasan, signed solely for this game, claimed four for 97 and Dan Worrall three for 41.
Needing to close a 24-point gap on their opponents at the start of play, Somerset made a poor start when Lewis Goldsworthy was bowled by the second ball of the match, a Kemar Roach inswinger that clipped off stump.
Archie Vaughan was promoted to form a new opening partnership and the 18-year-old son of England Ashes winning captain Michael Vaughan looked more than up to the task as his side set about recovering from the early shock.
He and Tom Lammonby took the score to 33 before Lammonby, on 21, fell to Jordan Clark’s first delivery of the game, a ball that bounced more than he expected and forced an edge to Dom Sibley at second slip.
Vaughan, who had taken 18 balls to get off the mark, appeared commendably unperturbed in batting through the morning session to be unbeaten on 44 from 105 deliveries at lunch.
He was given a life on 41 when Sibley failed to hold a sharp slip chance, diving to his right, off Tom Curran, making his first Championship appearance for nearly two years.
Abell, seeking to build on hundreds in the previous two Championship home games, again played with confidence and was 27 not out at the interval, with Somerset having recovered to 93 for two. But hopes that the third-wicket partnership would flourish in the afternoon session were soon dashed as Worrall had Vaughan caught behind off the second ball, edging a defensive push.
Heavily depleted by international call-ups, Surrey were relying heavily on the experienced Shakib. Emerging from a watchful start, Banton reverse swept him from two boundaries in an over.
Abell became Shakib’s first victim when he played back to a delivery that skidded through and bowled him one short of a half-century. Banton went to fifty off 90 balls, with 6 fours, and found a reliable partner in Rew as the pair blossomed in the afternoon sunshine.
By tea, they had taken the total to 197 for four, with Banton 65 not out, having survived a difficult chance to slip on 59. Rew was unbeaten on 16 and the final session saw both players prosper.
Banton reverse swept Cameron Steel for four and pulled his next ball for six to move into the nineties. He earned Somerset’s first batting point with a two off Curran and the following over from Clark saw him edge a single, raising both arms as he ran to celebrate a 132-ball century.
Content to play a supporting role, Rew brought up the hundred partnership off 137 balls in moving to 35 with a single off Curran and at 255 for four Somerset were building a position of strength. With seven added, Rew played forward defensively to Curran and edged through to wicketkeeper Ben Foakes.
It was 264 for four when the second new ball was taken at the earliest opportunity. Worrall struck a key blow when Banton launched a big hit at a slower ball and was bowled, having faced 172 balls. The following over from Shakib saw Kasey Aldridge fall in similar fashion and Craig Overton stumped, to strangely attacking shots in the circumstances.
When Lewis Gregory was bowled by Worrall for a duck, Somerset had lost four wickets in the space of 14 balls. Kiwi seamer Brett Randell was last man out on debut for three, Shakib and Surrey ending the day on a high.