The New Zealand striker gave Forest an eighth minute lead, when he finished a superb piece of play at the City Ground.
However, Liverpool substitute Diogo Jota's second-half header earned the visitors a battling 1-1 draw.
The result keeps Liverpool six points clear at the top of the standings, ahead of Forest, who move into outright second - although Arsenal can overtake them tomorrow morning.
Liverpool, whose only league defeat this season prior to their trip to the East Midlands came against Forest in September, looked to be heading for another humbling, before Jota's 66th-minute equaliser from a corner.
Jota and Mohamed Salah went close to snatching victory for Liverpool, but found home goalkeeper Matz Sels in inspired form.
"I could not have asked for more," Slot said. "Second half was outstanding. There are not many teams that can create so many chances against an opponent so defensively strong. Unfortunately we couldn't get a second.
"It is so, so hard for every team to create here. And at times it was one chance after another. That's why it was such a disappointment to go 1-0 down. I have to be pleased with what we got."
MEMORY LANE
The fixture recalled memories of the late 1970s and early 1980s when Forest would regularly compete for the English top-flight title with Liverpool.
This season, Nuno Espirito Santo's Forest side unexpectedly find themselves chasing the Merseysiders down once more, coming into today's clash on the back of seven wins in a row in all competitions, without conceding a goal in the last five.
Out to do the league double over Liverpool for the first time in a season since 1963, Forest edged in front as Wood continued his fine form with his 13th league goal of the campaign.
The visitors were seeing all of the ball but not doing a great deal with it. In the opening period alone, Liverpool enjoyed 70% possession, while failing to find the target.
Forest continued to stand firm, with home supporters dreaming of being in touching distance of their illustrious opponents, only for Jota to be left unmarked to level 22 seconds after coming off the bench with his first touch.
Three superb saves from Sels preserved a deserved point for Forest, who remain Liverpool's closest title rivals.
Forest supporters, however, having seen their side keep the league leaders at bay for so long, will view the draw as a missed opportunity.
"Tonight was a lesson for us, because this is how we want to compete," Nuno said. "I am very proud of how we played.
"Tonight was a special atmosphere. I don't look at the league table at this stage, we have to keep going."
Chelsea salvage point at Bournemouth
Chelsea captain Reece James rescued a point for his side with a 95th-minute free kick to snatch a 2-2 draw at home to Bournemouth.
Second-half substitute James, playing his first league game since November because of injury, beat goalkeeper Mark Travers with a perfectly placed curler into the far corner of the net.
But it was two points dropped for the hosts who dominated much of the game, scoring through Cole Palmer in the first half before Bournemouth replied with a Justin Kluivert penalty early in the second period and Antoine Semenyoput them ahead.
Chelsea, who have failed to win in their last five league games, stay in fourth place in the table on 37 points from 21 matches, with Bournemouth seventh on 34.
"I think we had a few clear-cut chances that we should have taken in the first half and put the game to bed," James told TNT Sport. "It's mixed emotions."
Palmer scored his 14th league goal this season after receiving a neatly weighted ball from Nicolas Jackson who had squirmed free of three midfielders on the halfway line.
Chelsea talisman Palmer then sent Travers to the floor with a little dummy and rolled the ball into his net.
The hosts had several first-half chances to double their lead, through Jackson, Palmer and Enzo Fernandez.
But they let the visitors back into the game three minutes into the second half when Moises Caicedo brought down Semenyo and Kluivert sent Robert Sanchez the wrong way from the spot.
City throw away two-goal lead
Manchester City threw away a two-goal lead as Brentford's Yoane Wissa and Christian Norgaard scored late goals to earn the hosts a 2-2 draw.
After suffering six league defeats in November and December, City bounced back with a draw against Everton and wins over Leicester City and West Ham United. But today's late collapse brought their short-lived revival to an abrupt halt.
The point leaves them sixth on 35, 12 adrift of leaders Liverpool, who drew 1-1 at second-placed Nottingham Forest, while the Bees are 10th on 28 following an unlikely comeback.
After struggling to create chances in the first half, City winger Savinho went close to breaking the deadlock in the 50th minute, marauding forward through the left channel before thumping a shot off the foot of the post.
Two minutes later City striker Erling Haaland headed straight at the keeper when he should have scored.
The breakthrough finally came for City in the 66th minute when a brilliant ball from the right by Kevin De Bruyne was met by Foden, who steered a deft volley in at the far post.
The game should have been over when Foden made it 2-0 12 minutes later by reacting quickest to rattle home the rebound, after Savinho's shot was saved, to silence the home fans.
Four minutes later, however, Brentford's Wissa ensured a nervy finish when he fired in from close range to reduce the deficit and, with City's defenders having made several last-ditch interventions to protect the lead, they should have been aware of the threat posed by the hosts.
But Denmark international Norgaard was allowed to complete the comeback two minutes into added time, getting enough power on his glancing header to send it past Stefan Ortega, despite the City keeper getting a strong hand to it.
Irons beat London rivals
West Ham United rode their luck to beat charitable London rivals Fulham 3-2 at the London Stadium in new manager Graham Potter's first Premier League match in charge.
A fluent Fulham side dominated the derby but failed to take their chances and gifted the hosts two goals, the second of which scored by Lucas Paqueta proved to be the winner.
Fulham, for whom Alex Iwobi scored twice, will wonder how they left pointless but Potter will not care as he enjoyed a victory on his home debut.
Victory lifted West Ham two places to 12th with 26 points while Fulham's first defeat in nine league games left them in ninth spot with 30.
Potter had been out of the game since he was sacked by Chelsea in April 2023, choosing to resume his career at West Ham. On arriving in east London he said it felt like Christmas and Fulham offered up some late presents.
