Forest opened the scoring early when Chris Wood's header slipped past Sam Johnstone in his first start for Wolves, but the visitors were level just two minutes later through a Jean-Ricner Bellegarde thunderbolt.
The remainder of the first half saw both sides trading control of the game, with each team creating, but ultimately failing to capitalise, on several promising chances.
Forest had a strong start to the second 45 minutes, pinning Wolves in their half and looking the more likely side to break the deadlock and retake the lead.
Gary O'Neil's double substitution on the hour mark sparked his side into life, leading to their first real threat since the restart and coming closest to scoring when Matheus Cunha's curling effort whistled just wide of the post.
The hosts thought they had found the winner through an instinctive finish from Wood in the 84th minute, but the goal was quickly ruled out due to a narrow offside, much to the dismay of the home fans.
Despite an additional 10 minutes of play at the end of 90 minutes, neither side managed to find a second goal, leaving the game tied at 1-1 and the points shared.
NOTTINGHAM FOREST VS. WOLVERHAMPTON WANDERERS HIGHLIGHTS
Chris Wood goal vs. Wolverhampton Wanderers (10th min, Nottingham Forest 1-0 Wolverhampton Wanderers)
A deep corner is aimed at the back post from Elliot Anderson and finds Wood, who is completely unmarked and sends his header across goal towards the far post.
Johnstone looks certain to make a routine save, but Wolves' new goalkeeper flaps at the header as it bounces into the far corner.
Jean-Ricner Bellegarde goal vs. Nottingham Forest (12th min, Nottingham Forest 1-1 Wolverhampton Wanderers)
A poor touch from Mario Lemina drops into the path of Bellegarde, who has space and time just outside the area as the Nottingham Forest defenders back away.
The midfielder turns and unleashes an unstoppable first-time strike into the top right corner, giving Matz Sels no chance and instantly drawing Wolves level.
MAN OF THE MATCH - ELLIOT ANDERSON
Anderson was instrumental in nearly all of Forest's promising attacks, making three key passes and delivering a brilliant corner for Wood to score the opener.
Not only was the midfielder pivotal in attack, but Anderson also made a significant defensive impact, winning seven ground duels and making four tackles.
A shoutout must also go to Cunha, who consistently troubled the Forest defence, creating one big chance and making two key passes throughout the encounter.
NOTTINGHAM FOREST VS. WOLVERHAMPTON WANDERERS MATCH STATS
Possession: Nottingham Forest 52%-48% Wolverhampton Wanderers
Shots: Nottingham Forest 16-11 Wolverhampton Wanderers
Shots on target: Nottingham Forest 5-3 Wolverhampton Wanderers
Corners: Nottingham Forest 7-3 Wolverhampton Wanderers
Fouls: Nottingham Forest 15-18 Wolverhampton Wanderers
BEST STATS
WHAT NEXT?
Following the 1-1 draw between Nottingham Forest and Wolves, both sides will be out of action for two weeks as the Premier League takes a break for the first International break of the campaign to take place.
When league football resumes, Nottingham Forest will face a challenging trip to Anfield to face Liverpool, while Wolves will host Newcastle United at the Molineux Stadium.