Resuming day two on 71-0, Notts lost regular wickets and had slumped to 175-6 when Alex Hales was out for 85.
However Read fought back with his 137-ball knock to take the visitors to 330 all out, a first innings lead of 61.
Worcestershire then lost four wickets, including stand-in skipper Alex Gidman for 21, as they closed on 115-4.
After England opener Hales was bowled by Jack Shantry, Notts still trailed by 94 with just four wickets in hand.
But Read's innings, which included 12 fours and a six, along with Ben Hutton's 40 and a rapid 38 from Jake Ball gave the away side a slender advantage.
Hutton then did the damage early in Worcestershire's second innings, taking two of the four wickets to fall, but teenager Joe Clarke (43 not out) and Ross Whiteley (22 not out) steadied things with a stand of 47.
Nottinghamshire captain Chris Read hit a crucial 90, before late wickets put his side on top against Worcestershire in their Championship game at New Road.