Somerset 216 (Trescothick 50, Groenewald 5-30, Palladino 5-97) and 145 for 6 (Compton 56, Clare 5-29) beat Derbyshire 266 (Johnson 56, Madsen 50, Overton 3-35, Thomas 3-54) and 94 (Kirby 4-18, Meschede 3-17) by four wickets
Nick Compton lifted Somerset with a vital half-century that guided them to a tense four-wicket at Derby and left Derbyshire bottom of the LV= Championship First Division.
But Compton found bad news almost as soon as he left the field. While Somerset celebrated their first Championship win of the season, Compton was omitted from the England side to face Essex in an Ashes warm-up at Chelmsford at the weekend. Joe Root was chosen to open the innings
Compton made 56 in front of National Selector Geoff Miller but even as he did so the ECB was preparing a statement carrying Miller's assertion that Root, not Compton, was the opener best suited to join Alastair Cook at the top of the order.
Derbyshire's problems were compounded when they were bowled out for 94 early on the final day. Jon Clare took 5 for 29 in eight overs to launch a fightback, but Somerset reached their target of 145 to get a disappointing season underway
Steve Kirby had earlier taken 4 for 18 and Craig Meschede 3 for 17 as Derbyshire lost their last eight wickets for 56 to be bowled out for 94 and remain at the foot of Division One.
They had gone into the fourth day strongly placed with a lead of 86 and eight wickets intact but only two more runs had been added when Somerset got the big wicket of Shivnarine Chanderpaul, who dabbed Alfonso Thomas into the hands of third slip.
It was a poor stroke by the experienced West Indian but there was plenty of seam and swing movement to make life difficult for the batsmen and Meschede blew away the middle order with a burst of 3 for four in 12 balls.
Billy Godleman was caught behind as he pushed forward, Ben Slater was bowled first ball, and Richard Johnson gave Alex Barrow another catch to leave Derbyshire in deep trouble at 54 for 6.
The next blow was self-inflicted as Clare wandered down the pitch and was run out by Jamie Overton's direct hit from mid-on but former Somerset batsman Wes Durston and Tony Palladino gave Derbyshire hope by nudging the lead towards 150.
They added 26 in nine overs but the introduction of Kirby at the City End saw the last three wickets fall for just four runs. Palladino edged to second slip, Tim Groenewald could only fend a lifting ball to first slip and after Durston carved Overton over the slips for four, he was bowled going for a big drive.
It had been an impressive morning's work by the Somerset seamers but their batsmen knew the target would not be a formality in conditions that favoured the bowlers.
Derbyshire knew they needed to strike early to spark panic in the visiting camp but Marcus Trescothick and Compton reduced the target by 30 in five overs before lunch, with Compton pulling Mark Footitt for six.
The pair took their stand to 60 before Trescothick was caught at cover off a leading edge off Clare and although Compton was looking increasingly assured, it was a different story at the other end.
Dean Elgar flashed at Clare and was caught at first slip, James Hildreth offered no shot and was lbw for three and although Craig Kieswetter drove his first ball through the covers for four, he was caught behind off the next to leave Somerset wobbling on 102 for 4.
When Compton edged a big drive at Clare to first slip seven runs later, Derbyshire sensed they could still pull off an unlikely victory but Peter Trego settled Somerset's nerves with some aggressive strokes to carry his side home with 41 overs still to bowl.
Somerset took a vital 20 points to ease their relegation worries, while Derbyshire collected just five.