The defending champions were all out for 282 on day one, but were 51-6 at one stage during the morning session.
Hodd put on 132 with Azeem Rafiq (74) and 88 with Jack Brooks (48) but was left on 96 not out when Brett Hutton (3-67) had Ryan Sidebottom lbw.
Notts lost Jake Libby and debutant Tom Moores as they closed on 38-2 in reply.
Yorkshire went into the game second in the table, but needing a victory to close the 26-point gap between themselves and leaders Middlesex, who are not playing this week.
Steven Mullaney (3-57) ran out Adam Lyth backing up in the ninth over and then proceeded to remove Alex Lees, Jake Lehmann and Tim Bresnan with his medium-pace.
Hodd and Rafiq, who was capped during the day, led the fightback over the next 33 overs before the latter was lbw to Samit Patel.
Brooks, however, played his part in their revival with his highest score of the summer before sending back Libby lbw with his opening delivery of Notts' reply, and Bresnan had Moores caught at slip with the final ball of the day.
Andrew Hodd ran out of partners just short of a century after rescuing Yorkshire from a dismal start to their Championship game at Scarborough.