Somerset 137 (Barker 5-32) and 102 for 2 (Dickson 63*) need 400 runs to beat Hampshire 308 (Dawson 115, Brook 5-56) and 330 for 3 dec (Gubbins 139*, Vince 63, Middleton 52)
Nick Gubbins effortlessly struck his third LV=Insurance County Championship as Hampshire ground Somerset towards submission on day three at the Ageas Bowl.
Left-handed batter Gubbins gracefully hit an unbeaten 139 - his highest score for Hampshire since joining from Middlesex - to move past 900 runs in the Championship this season.
Together with Fletcha Middleton and James Vince's half-centuries, Gubbins led Hampshire to a 501-run lead having forced Somerset to wallow in the south coast heat.
Facing a minimum of 128 overs to bat out, the visitors slumped to 38 for 2 but Sean Dickson's unbeaten 63 held them together. They reached the close on 102 for 2 with 400 still required to win.
Hampshire's title ambitions had been ended by 11am by Surrey's victory over Warwickshire.
Their openers Toby Albert and Middleton had tediously scored 45 runs in 23 overs the previous evening, but their lack of adventure paid dividends, having taken much of the lacquer off the ball. They batted with more intent as they took their partnership to 80 with little fuss, Middleton reaching his fourth fifty in his debut season.
They both fell within four overs of each other, Middleton bowled two balls after reaching the milestone and Albert was caught and bowled by New Zealander Neil Wagner, on his Somerset debut.
Gubbins had been incredibly slow, on an even slower pitch, in the first innings to take his seasonal strike rate to the third lowest in Division One - only Dom Sibley and Luke Proctor were slower for those who had scored more than 200 runs.
This time around he showed an attacking flair, taking part of a cover-drive battle with Vince as he reached 50 in 81 balls. The 135 balls his subsequent century came in, were the fastest of his six tons for Hampshire.
Lewis Gregory, although on the pitch, was not used at all on day three, while fellow opening bowler Jack Brooks only bowled five overs before the declaration.
As such, Gubbins and Vince - whose 50 came in 66 balls - found the going easy with little pressure built to stop them from scoring at will. The run rate from the morning session 3.94 before moving to 4.97 in the afternoon.
Vince was caught from behind to end a 162-run stand, but Tom Prest picked up where he left off to continue the flow of runs with Gubbins - who is enjoying the second-best Championship season of his career. The pair added 79 together before the long-awaited declaration came at tea.
Liam Dawson was the main worry for Somerset, with the occasional spin more threatening than pace on a feather-bed. And it came to pass as the left-armer had Tom Lammonby stumped with his third delivery.
Tom Abell followed when James Fuller's extra pace was edged to second slip, where Vince took a sharp catch.
Dickson and Andy Umeed showed tenacity and a backbone vital to save Hampshire from defeat. Dickson, in particular, looked in good order to reach his half-century in 86 balls.
