Acting manager Mick Harford must have felt his side were on the way to clinching all three points in his first game in temporary charge as he looked to claim a stake for a permanent stay in the hot-seat.
Michael Dawson had put the home side ahead 11 minutes after the interval following constant first-half pressure by the Foxes only to see his team's lead disappear deep into stoppage-time.
It was the Forest captain's first goal of the season after a disappointing start to the campaign caused by a lengthy lay-off through injury.
It seemed that the disappointment of the thumping defeat at the hands of Derby County last weekend had been put behind them and a spirited second-half performance by the hosts was going to be enough to secure a much-needed win.
City were unlucky to be level at the half-time break after Connolly had squandered three splendid chances, the first of which came after only 30 seconds.
The home side were quickly out of the blocks in the second half and were rewarded with the opening goal. Andy Reid curled in a corner, and after the ball was chested down by Adam Nowland, Dawson thumped the ball into the roof of the net from only six yards out.
Leicester were unable to unlock the home side's defence until two minutes into stoppage-time. A long free-kick from the halfway line was flicked on by Dion Dublin for Connolly to tap in and make amends for his miss in the first minute.