He was in the right place when Ian Breckin flicked on a right-wing corner from Nicky Southall and half-volleyed the ball first time past a helpless Mildenhall.
The goal - Grant's fifth of the season - lifted Colin Calderwood's team three points clear of Tranmere at the top of the table, and sent the Glovers to their first home defeat since Russell Slade took charge.
Forest have still conceded only two goals in their first seven outings, and keeping another clean sheet must have delighted their manager as he lost two of his three central defenders before half-time.
Both Danny Cullip and John Curtis were forced off with injury, and Forest switched to a back four to hold off Yeovil's attacks, which were frequent but often lacked venom.
Holt brought the first good save from Mildenhall in the fifth minute and the ex-Grimsby keeper was in action later in the half to block a close-range effort from Jack Lester.
On one occasion when Mildenhall was beaten, Breckin joining in late with the attack to held goalwards from a corner, the keeper was saved by a defender's head as the ball was about to cross the line.
Yeovil's best chance came on 50 minutes and they should have scored. The experienced Marcus Stewart, playing in front of home fans for the first time since a loan move from Bristol City, found a gap in the defence to put Wayne Gray in the clear.
The ex-Southend man was in a central position with only Paul Smith to beat but fired straight at the keeper's legs.
More pressure had to be withstood at the other end with Mildenhall making the save of the day from a Neil Harris header in the 70th minute. A few minutes earlier Lester had also brought the best out of the giant home keeper when put clear by a right-wing free-kick.