Somerset 284 (Gregory 65, Barnard 3-54, Hannon-Dalby 3-76) and 180 for 6 (Lammonby 66*, Hannon-Dalby 3-21) drew with Warwickshire 392 (Hain 119, Davies 118)
Warwickshire's seamers gave Somerset a final day scare before the LV= County Championship match at Taunton ended in a predictable draw.
Somerset took nine points and Warwickshire 11 from a contest ruined by the first-day washout at the Cooper Associates County Ground.
A draw appeared the most likely outcome when play began and interest initially centred on the battle for bonus points, with Warwickshire needing 93 off 21.4 overs to reach 400 and Somerset four wickets in the same period to claim maximum bowling points.
Hain and Burgess built steadily on the overnight lead of 23 until with the total on 321, Burgess, who had added ten to his score of 36 at the start of play, advanced down the pitch to Peter Siddle and was bowled.
Jacob Bethell arrived at the crease looking to increase the tempo. He lofted Jack Leach back over his head for six and took a single off the next ball to take the score to 350.
Warwickshire had just under seven overs to add another 50 for maximum batting points, but their hopes suffered a blow when Bethell was bowled by Josh Davey for 19, swinging to leg.
Hain reached a rock-solid hundred when a quick single to mid-on turned out to add five to his score as Overton's throw at the stumps brought four overthrows. It was reward for more than four hours of concentration by Hain, who had faced 254 balls and hit 10 fours.
Hasan Ali launched a six over long-on off Davey and Hain also went on the attack before, with the total on 389 for 7, he was caught behind aiming a back-foot forcing shot off Leach.
Somerset skipper Lewis Gregory brought himself on for the 110th over, with his side needing one wicket and Warwickshire nine runs to register another bonus point. It proved a shrewd move as Hasan, on 15, pulled a catch to Tom Kohler-Cadmore at mid-on and Rushworth lifted a catch to Overton at long-on.
Warwickshire had the consolation of a 108-run lead, with Somerset's openers facing a tricky three overs before lunch. They failed to negotiate it, Sean Dickson edging Hannon-Dalby to first slip where Rob Yates took his fifth catch of the match.
Somerset were one for one at the interval and dressing room nerves in increased in the first over of the afternoon when Cameron Bancroft registered the second duck of the innings, pinned lbw by Hannon-Dalby.
Kohler-Cadmore, fared little better than fellow debutants Dickson and Bancroft, scoring 16 before edging Rushworth to Hain at second slip to make it 25 for 3.
When George Bartlett had his middle stump uprooted by Hasan, having made 20 and with the total on 62, Somerset were in serious trouble. There were still 58 overs to be bowled and they trailed by 46 runs.
With the deficit reduced to 16, James Rew was bowled for 14 looking to pull a short ball from Rushworth, starting a new spell having switched to the Marcus Trescothick Pavilion end.
It was 112 for 5 at tea, Somerset leading by just four. Lammonby had played well for his 46, but there were still a possible 42 overs to navigate.
The final session saw Gregory bowled by Hannon-Dalby for 26 with his side only 19 ahead. Lammonby went to a priceless fifty off 83 balls, with six fours, and at 132 for 6 the floodlights were switched on.
Mindful that bad light had ended play nine overs early on day three, Warwickshire employed spin at both ends. But Bethell and Yates could not force another breakthrough.
Overton was dropped on 13 by Hannon-Dalby at mid-on off Bethell before the players shook hands at 5.15pm. Lammonby had faced 120 balls and hit seven fours and a six.