Nottinghamshire 166 (Edwards 6-50) and 128 for 4 require a further 383 runs to beat Hampshire 277 (Vince 74, Dawson 72, Abbott 60*) and 399 for 7 (Vince 149, Alsop 99, Footitt 3-69)
Liam Dawson took two of four Nottinghamshire second innings wickets as Hampshire were held up in their quest for their second Specsavers County Championship victory of the season.
Dawson's spin managed to dismiss Chris Nash and the impressive Kraigg Brathwaite, with Kyle Abbott and Fidel Edwards also celebrating wickets - but Riki Wessels and Steven Mullaney showed off some brilliant defensive batting to give Nottinghamshire hope of saving a draw.
Hampshire had set Nottinghamshire an improbable 511 to win, or a more likely 156 overs to bat out after Tom Alsop had fallen an agonising one run short of a second first-class century.
Alsop had begun the day on 63, having provided the anchor for James Vince's magnificent 147 the previous evening, and continued in a watchful manner with Rilee Rossouw.
A century had looked inevitable with his carefully calculated flicks to the legside and occasional pushes into the offside slowly pushing his score towards three figures.
No risks were taken by the 22-year-old during the 74-run stand with Rossouw - who punished the bad balls as he sensibly kept the score ticking to allow Hampshire to declare whenever they wanted.
With the sun baring down on a slow wicket, which seemed to be getting slower, the Nottinghamshire attack were forced to toil for an hour with the old ball.
But the new ball worked within five overs as Luke Fletcher pinned Rossouw lbw for 36.
Alsop almost scored his maiden ton against Nottinghamshire at Trent Bridge in 2016, but fell for 93, and his 'nineties hoodoo' against Nottinghamshire struck again.
Mark Footitt dragged short and outside his off-stump for his 196th ball and the left-hander jabbed unconvincingly straight to Matt Carter, who took a fine low catch at point.
Gareth Berg fell soon after to Footitt as the ball stuck in the pitch to lob a simple catch to short extra cover.
Abbott and Dawson added 133-runs for the eighth wicket in the first innings, and set about a similarly important accumulation with the duo putting on an unbroken 63. And with the lead reaching 511, Vince decided to call in the pair and declare.
That left Nottinghamshire needing an unlikely 511 to win, or the more probable option of batting out 156 overs, on a slowing wicket under clear blue skies.
Hampshire were without fast bowler Dale Steyn due to a groin injury sustained while bowling in the first innings - the South African underwent a scan during the afternoon with a short five day lay-off expected, although not yet clear.
It appeared the hosts would miss their talisman when Brathwaite and Jake Libby dealt with new ball bowlers Fidel Edwards and Berg with defensive resolve.
But Abbott joined the attack and in the 13th over and found a delivery to keep low to Libby and with some inward movement saw the opener's off-stump cartwheel backwards.
Nash was bamboozled by Dawson, as the left-arm spinner got one to straighten onto the former Sussex man's pads, before Samit Patel tentatively pulled Edwards to Rossouw at mid-wicket.
West Indian debutant Brathwaite maturely blocked and managed the game well with 48 from 123 balls, but ballooned a forward defensive off Dawson up to Berg at gully.
Wessels, who suffered a nervy moment when he was dropped by Edwards on 12, and Mullaney took almost 20 overs out of the match to reach close still needing 383.