Wagh miscued Rashid to mid-on and Ajmal Shahzad produced some fireworks to account for both Samit Patel and Ali Brown.
Voges battled on, adding 38 with Chris Read, but fell to Hannon-Dalby four overs before the new ball was due.
But Read, dropped on seven by Yorkshire wicketkeeper Gerard Brophy, ensured there were no further alarms, seeing Notts to the close in the company of Darren Pattinson.
BBC Radio Nottingham's Dave Bracegirdle: "In many ways it was a day of frustration for Nottinghamshire supporters because the batsmen showed all the fight and character that was lacking in the first innings.
"Having polished off the Yorkshire tail inside the first 10 minutes, they set about chasing a 205-run deficit.
"Paul Franks made a season's best 79 and coupled with 90 from Mark Wagh and 72 from Adam Voges, Notts put themselves in a position to make Yorkshire bat again.
"However, late wickets in the day saw the home side close on 357-6, an overall lead of only 152."
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