Notts County and Wrexham both enjoyed slender leads during the action-packed game, before goalkeeper Ben Foster (40) saved a penalty in stoppage time to ensure the hosts held on to claim victory courtesy of Elliot Lee's (28) 78th-minute winner.
Wrexham, owned by Hollywood stars Ryan Reynolds and Rob McElhenney, are top of the fifth-tier National League with 103 points from 42 matches, while second-placed Notts County have 100 points and have played one more game.
Wrexham, who need seven points from their remaining four games to secure promotion, next travel to Barnet on Saturday. Only one team earns automatic promotion to League Two.
"We're not going to get carried away. It's a really important victory but we can get our feet back tomorrow for training," Wrexham manager Phil Parkinson said.
