Eze opened the scoring from the penalty spot on the hour mark, coolly converting to notch his 10th goal of the season. Just four minutes later, Forest responded when Murillo diverted a powerful strike from Neco Williams past Dean Henderson, denying Palace a deserved lead.
The Eagles were the dominant side for much of the contest, creating the better chances and applying sustained pressure.
Eze nearly clinched all three points late on, rattling the crossbar with a thunderous long-range effort that had the Forest goalkeeper beaten.
His performance was not only crucial on the day but also historic - Eze has now become the first Crystal Palace player since the club's promotion in 2013/14 to register double figures in both goals and assists in all competitions within a single season.
"I think we had quite a few chances at the end. I thought we were going to take it at the end, but I think a point, we'll take it," Eze told Sky Sports.
"We're positive, we know we put in a good performance today.
"We had quite a bit of time off, but I think the boys were top today to come back. It was a high emotion game a week ago, so to put in a performance like this today was important for us."