Alex Hales hit his maiden LV= County Championship century to ensure that Notts remain in contention to preserve their winning start.
Notts were all out for 315 in their second innings, setting Hampshire a victory target of 281 in their run chase which they begun by reaching 7-0 at stumps.
Hales drove a Dominic Cork slower ball to cover on 136 but had underpinned a recovery from 125-5 to 220-6 alongside club captain Chris Read.
His knock included 15 fours and was punctuated by a six over long-on to bring up three figures.
Nottinghamshire's opening batsmen will be under scrutiny when Mark Wagh returns to the team to face Essex with Mick Newell keen to back Hales.
"Alex didn't have the best pre-season and perhaps presumed that he would be in from the start but I had to get across that some of his performances in the nets weren't good enough," said Nottinghamshire Director of Cricket Mick Newell.
"His methods of practice and preparation have improved dramatically since then and he has capitalised on this opportunity.
"We're looking for runs in the top three and Mark Wagh has been pretty consistent so I'd expect him to return to the side, Alex to move up the order and then we've got a decision to make on who misses out."
Edwards (23) and Shafayat (14) shared an opening stand of 25 and low scores from Samit Patel (0), Steven Mullaney (7) and Ali Brown (15) put Notts in a precarious position.
Notts were 293-7 when Paul Franks edged Dominic Cork to Nic Pothas for a quickfire 45 and Andre Adams ended unbeaten on 26.
All three results are possible on the final day with Notts keen to press for a fifth consecutive LV= County Championship victory.