McLeish, appointed on Thursday after the Al Hasawi family dispensed of Sean O'Driscoll's services on Boxing Day just hours after the 4-2 home win over Leeds, received a good reception prior to kick-off at the City Ground.
Andy Reid scored Forest's first goal of the McLeish era, equalising in first-half injury time after Glenn Murray had put Palace in front in the ninth minute.
It looked like there was to be no fairytale beginning for the Scot when Murray struck again with nine minutes remaining, but Sharp grabbed an injury-time leveller.
Dexter Blackstock headed an early chance wide for Forest before Murray opened the scoring.
Dean Moxey got to the byline, his low cross evaded everyone and Murray bundled the ball home at the far post.
Julian Speroni preserved Palace's lead in the 15th minute, sprawling to his right to tip Radoslaw Majewski's shot wide.
When Speroni was beaten by Sharp's diving header just before the half-hour mark, the post came to Palace's aid.
Forest were enjoying some good pressure and finally got themselves level at the end of the first half with a superb 25-yard shot from Reid that flew across Speroni and into the bottom left-hand corner of the net.
Wilfried Zaha came close to putting Palace back in front at the start of the second half but his shot fizzed across goal and narrowly missed the far post.
At the other end, Speroni continued his good afternoon with another fine save to keep out Chris Cohen at the near post.
The Argentinian was at it again midway through the second half, this time pushing away Danny Collins' header.
Murray got his second goal of the game with a superb 81st-minute header.
Yannick Bolasie's far-post cross looked to have evaded Murray, but the striker somehow generated enough power to loop the ball back across goal, over goalkeeper Lee Camp and into the back of the net.
It looked like giving Holloway's team their first win in five npower Championship matches but there was time for more late drama.
Speroni produced a superb save from Blackstock's header to tip the ball onto the post, but Sharp was on hand at close range and had the simplest of finishes to earn Forest a point.