They slipped to eight for two in the fifth over, but Dale Benkenstein and Michael Di Venuto then put on 95 in 29 overs and Durham were 113 for four when a halt was called at 5.30pm
They suffered a second burst of the jitters when, with the game apparently safe, the experienced third-wicket pair fell in quick succession.
Benkenstein pulled his ninth four in front of midwicket to reach 50, but went to drive the next ball from Peter Trego well wide of off stump and got a big inside edge onto his stumps.
There were only 19 overs left at that point, and Ben Harmison survived a first-ball lbw appeal before Di Venuto departed in the next over.
Showing rare restraint, he had reached 44 off 107 balls when he was caught off bat and pad at short leg off Ian Blackwell’s left-arm spin.
Harmison and Phil Mustard blocked out the next eight overs before Somerset settled for the draw which had always looked likely after the first four sessions were lost to the weather.
Somerset’s earlier declaration on 193 for five appeared to be pre-determined. Having crawled to 16 for none in nine overs the previous evening, they took 14 off Graham Onions’ opening over of the day.
Marcus Trescothick continued to blaze away, adding 44 off 39 balls to his overnight six, before he was lbw trying to sweep off-spinner Paul Wiseman’s second ball.
Somerset promoted Trego to number three and after he hit 30 off 28 balls they appeared to decide they were getting ahead of themselves, not wishing to set Durham more than 300 in the belief they would not go for it.
The fourth-wicket pair of James Hildreth and the big-hitting Blackwell rarely opened their shoulders in adding 68 in 19 overs before both fell with the declaration looming.
Blackwell drove Wiseman to long-on and Hildreth had faced 96 balls for his 46 when he edged Steve Harmison to give Di Venuto his third catch at slip.
Following his half-century in the first innings, Durham opener Mark Stoneman made only one before edging Steffan Jones to wicketkeeper Craig Kieswetter.
Then in the next over Will Smith edged left-armer Charl Willoughby to second slip when aiming to leg. But the dependable Benkenstein’s sixth championship half-century of the season virtually ended Somerset’s victory hopes.