Will Kendall and Robin Smith restored some pride to Hampshire's batting by leading a spirited fightback in the final session at Taunton. Coach Jimmy Cook had demanded a more resolute approach after Piran Holloway's first century for almost a year enabled Somerset to build a first innings lead of 226.
And, after openers Andy Sexton and Giles White had fallen cheaply, an unbroken third wicket stand of 76 enabled Hampshire to close on 140-2, with the deficit reduced to just 86.
Kendall smacked 10 fours in reaching only his second Championship half-century of the season and finished unbeaten on 74, while skipper Smith looked increasingly menacing as he move to 35 not out.
It was a welcome relief to Cook, who was backing his side to produce a vast improvement on their woeful first innings effort of 142.
"Away from home we have found opponents guarding against Shane Warne by leaving some grass on the pitches and our batsmen have lost confidence by being rolled over on some poor wickets," he said.
"This track is about the best we have encountered and I was interested in seeing how we performed in better weather than we encountered in our first innings. I told the players they should be looking forward to batting in such conditions."
By the closing overs Kendall and Smith were doing just that, with the latter producing some typically swashbuckling square cuts that were ominous for Somerset.
Hampshire still have some way to go to save the game. But, with the weather forecast poor for the final two days, the home side are no longer cast iron favourites.
They looked to be gaining a stranglehold on the match when Holloway and Mike Burns built a sixth-wicket stand of 110 after Somerset had resumed on 208-4.
Holloway was given a life after adding just two to his overnight score of 53 when John Stephenson dropped a catch running back from slip off a top-edged hook. Peter Hartley was the unlucky bowler.
It proved an expensive miss as the little left-hander went on make a typically determined 113, off 280 balls, with 12 fours, before edging a Warne googly to wicketkeeper Adrian Aymes.
Burns put a string a low Championship scores behind him, producing several well-timed cover drives in his fluent 56, an innings ended by a brilliant leg-side stumping by Aymes off seamer Dimitri Mascarenhas.
At 320-5 Somerset looked on course for maximum batting points. But Burns' departure saw the last five wickets fall for just 48 as Warne reaped the reward for 38 overs of perseverance on an unhelpful pitch with figures of 4-91.
The Australian never looked happy and was limping at times. But Cook is full of praise for his unstinting efforts.
Hampshire's second innings looked to be heading the same way as the first when Steffan Jones removed Sexton for four and White to the last ball before tea, lbw for 18.
At that point Hampshire were 64-2. But the final session belonged to them and a Somerset attack, lacking its spearhead Andy Caddick because of England duty, still has it all to do to capitalise on what appeared a winning position.