Ben Harmison took three wickets in four balls to help secure a 210-run victory for Durham that piles the pressure on title-chasing Notts in their two remaining fixtures.
Notts remain favourites to secure a first LV= County Championship crown since 2005 but their remaining fixtures against Yorkshire at Trent Bridge and Lancashire at Old Trafford now hold added significance.
Paul Franks replaced Samit Patel in an opening partnership that yielded 31 runs but Harmison struck to see Hales caught by Michael Di Venuto at second slip before Voges was caught behind by Phil Mustard. Samit Patel scored two from the next delivery before falling lbw as Notts slipped to 54-4.
Chris Read (0), Andre Adams (9) and Luke Fletcher also failed to make starts on a batting card that saw Darren Pattinson demonstrate his dedication by facing 13 balls for an unbeaten nought.
Steven Mullaney, Nottinghamshire's best batsman on the day, scored 64 before top-edging to Mustard who ran to third man to hold a comfortable catch that ended the contest with Notts all out for 180 in their second innings.