Paddy Madden and Matt Dolan scored either side of half-time, with Alan Judge equalising for County from the penalty spot in the 49th minute.
The Glovers started brightly with efforts on goal from Angelo Balanta and Ed Upson.
Notts replied through Yoann Arquin, but his header from Judge's cross did not have the power to beat goalkeeper Marek Stech, who produced a wonderful parrying save after 42 minutes to keep out Enoch Showunmi's header.
At the other end, teenager Fabian Spiess made a superb stop to deny Dolan, but Madden pounced on the rebound for his 22nd goal of the season in first-half injury-time.
Judge levelled things up for the home side early in the second half, picking himself up to send Stech the wrong way from the penalty spot after being fouled by Dan Burn.
But the hosts' joy was shortlived as Dolan's fiercely-struck 25-yard free-kick restored Yeovil's lead in the 52nd minute.
Jeff Hughes wasted a guilt-edged chance to equalise shortly afterwards, somehow missing from a couple of yards out as the Glovers won for the first time in six matches.