The visitors suffered a pre-match blow, with Emiliano Martinez having to pull out, but his replacement, Marco Bizot, was on hand to make the game’s first save as he tipped Neco Williams’ shot wide.
There was certainly an edge to proceedings due to the contest’s importance at both ends of the table, and the breakthrough eventually came through an own goal in the 23rd minute.
Morgan Rogers fizzed the ball into the six-yard box, where Murillo was unable to sort his feet and knocked it into his own net.
Seemingly buoyed by his role in the opener, Rogers then played a pass that forced Matz Sels to rush out to deny Ollie Watkins, who soon fired a shot of his own that glanced off the crossbar on its way behind.
Forest struck back in the 38th minute, though, as Callum Hudson-Odoi laid the ball off for Williams to drill a first-time strike past Bizot.
Williams then hit another attempt from outside the box, but was denied by the Villa goalkeeper, and a header went wide of the Dutchman’s post shortly before the break.
Igor Jesus had sent two attempts off-target within eight minutes of the restart, and Youri Tielemans struck wide at the other end with both sides showing intent.
The goalkeepers were forced to make an impressive save apiece shortly after the hour mark, as Bizot reacted well after Morgan Gibbs-White’s attempt took a touch off Matty Cash, before Sels got down to deny Watkins.
Sels then stopped Ross Barkley’s shot but parried it into a dangerous area, and will have been relieved to see Rogers blaze his shot over. When Williams delivered a corner that Chris Wood got his head on but couldn’t turn towards goal, the full-back latched onto the loose ball and hit a venomous shot that Tielemans blocked.
Villa carved out late opportunities to secure victory, but Watkins cleared the crossbar, and Cash’s ambitious strike was saved.
As a result, Forest extend their unbeaten run across all competitions to five matches, even if the draw leaves them precariously close to the relegation zone, with the Tricky Trees sitting three points ahead of Tottenham Hotspur.
Meanwhile, Aston Villa’s three-game winning run in competitive action was brought to an end, meaning they missed a chance to go above Manchester United.