Resuming on 300-3, Yorkshire seemed set for a mammoth total on a decent batting track with captain Andrew Gale and his predecessor Anthony McGrath at the wicket.
But in glorious conditions, Yorkshire's attempts to bat the home side out of the game were stifled by some disciplined home bowling.
After a fuss-free opening 10 overs in which McGrath moved without incident to 64, the former England batsman snicked James Tomlinson through to Nic Pothas who snaffled the catch.
Boundaries were scarce under cloudless southern skies but the Rose Bowl pitch was not showing any hidden demons and Yorkshire's march to a total nudging 500 still seemed on at 327-4.
But their previously reliable batting line-up quickly conspired to turn Hampshire's bowlers – also-rans on Monday – into apparent world-beaters.
Gale went just six runs after McGrath's dismissal, hurried out by a rejuvenated Dominic Cork for a well-constructed 56 to leave Yorkshire 333-5, with new batsmen Adil Rashid and Jonathan Bairstow both at the crease on nought.
A dismal morning session looked to be complete for the visitors when wicketkeeper Bairstow departed for four, edging the impressive Tomlinson to Pothas for his third victim of the day.
But with the score at 337-6 and a total of 400 looking less likely with each passing delivery, Rashid stepped in with an innings of breezy intent, the talented all-rounder racing to 46 not out at lunch.
He and Richard Pyrah moved Yorkshire onto 393-6 after the interval before Pyrah edged David Balcombe to first slip for eight, sparking Yorkshire's second mini collapse of the innings.
Rashid went for a neat 51 before tailenders Tino Best and Oliver Hannon-Dalby were quickly polished off as the innings limped to 415 all out.
Hampshire's reply got off to a solid if unspectacular start, England cap Michael Carberry and opening partner Jimmy Adams prodding and nudging Hampshire to 49-0.
Best apart, who looked impressive and bowled with his usual intensity – even in front of a sparse Rose Bowl crowd – Yorkshire's bowlers looked somewhat toothless, former Fashion Design student Steven Patterson in particular looking a cut or two below his best.
But as the sun threatened to bake a good pitch into a batsman's paradise so Rashid once more stepped in to stamp his authority on proceedings.
First Carberry went after advancing down the track to the leg-spinner, succeeding only in clipping the ball straight back and the England prospect took a neat return catch.
Former Yorkshire player Michael Lumb was next to the crease, and Rashid wasted no time in sending the England man – restored to Hampshire's ranks after a visit to Downing Street on Monday with his fellow World Twenty-20 colleagues – back to the pavilion.
After setting Lumb up with a couple of flighted deliveries, Rashid sent down a quicker, flatter delivery. Too full and too quick for the dangerous Lumb to pull, he succeeded only in top edging straight over wicketkeeper Bairstow's head and into the grateful hands of Jacques Rudolph who scampered from first slip to take a simple catch.
The wicket removed one of Hampshire's dangermen but brought the experienced and in-form Neil McKenzie to the wicket. In tandem with Adams, he put the brakes on a Yorkshire attack smelling blood and steered Hampshire from 49-2 to the relative safety of 143-2.
But Gale's side are nothing if not resilient and with the light fading they found an extra gear to reward a surprisingly large contingent of White Rose supporters.
Adams, who had moved serenely to within touching distance of a century, was dismissed by Hannon-Dalby for 82, Rudolph taking his second tidy catch of the innings.
Bad light eventually saw the day cut slightly short, and a draw would still seem the likeliest result on a placid track – but a Yorkshire bowling performance to rival Hampshire's early-morning burst yesterday could yet see Gale's men set up a potential win.