It was Forest's first away win of the season, and they moved out of the drop zone.
Before this match, Forest had only scored one away goal in the league.
Lyanco lost possession on the halfway line after Brennan Johnson raced clear and Taiwo Awon buried the chance.
In their 11th successive top-flight campaign, the Saints have only won once in 13 in the league since they beat the Blues.
Since Nathan Jones took over as manager, the Saints have not picked up a point from four matches.
As it stands, Forest are set to move up from 18th to 15th, as they have lost only two of 10 games in all competition.
The side with the worst home record against the team with the worst away record was shown before the match started.
Che Adams had a great chance to put the hosts in front after six minutes, but his shot was wide of the goal.
Forest, who had just two points from their previous eight games on the road, hit the woodwork through Johnson before Awoniyi opened the scoring.
The first half was even worse for the hosts when Armel Bella-Kotchap, a member of Germany's World Cup squad, went off injured after only 34 minutes with Duje Caleta- Car replacing him.
The team was booed off at the end of the first half as the atmosphere turned hostile.
Sekou Mara had a rare chance for the Saints in the second half but headed wide and was wrongly given a goal kick.
In the 64th minute, Jones made an attacking triple substitution with Joe Aribo, Samuel Edozie and Adam Armstrong all coming on.
The club's 24th signing of the season, a free transfer from Palmeiras, was given a debut by Forest.
The Forest players were happy to defend deep and frustrated the hosts with their defensive skills.
They lost their sixth successive league game and it was their worst run in two years.
Bhupinder Singh Gill became the first Sikh-Punjabi to serve as an assistant referee in a premier league match.
He said earlier that he hoped to inspire the future generation.
"My dream has always been to reach the top of the game, be a role model for future officials and encourage more people from diverse background into officiating, especially from a South Asian background just like me," he stated.