Paulo Fonseca's side responded positively to their recent defeat against Paris Saint-Germain, producing a controlled performance to overcome Angers and strengthen their position in the Ligue 1 standings.
Nuamah opened the scoring in the 38th minute before Tolisso sealed the victory with a second goal in the closing stages.
The result moved Lyon to third place with 17 points from nine matches, three points behind league leaders PSG and one behind Lille.
Nuamah breaks the deadlock
Lyon started the encounter with attacking intent, looking to put their recent disappointment behind them.
The hosts gradually established control and created opportunities against an Angers side that remained compact in defence.
Their persistence paid off in the 38th minute when Ernest Nuamah found the breakthrough to give Lyon a deserved 1-0 lead.
The Ghanaian forward's goal rewarded Lyon's attacking pressure and provided the hosts with an important advantage heading into the interval.
Tolisso seals victory with late header
Lyon continued to dictate proceedings after the restart, although Angers attempted to remain competitive and prevent the hosts from extending their advantage.
The visitors struggled to create enough clear opportunities to seriously trouble Lyon, who remained organised and patient in possession.
The decisive moment arrived in the 86th minute when captain Corentin Tolisso rose highest to meet a corner and headed the ball into the net.
The goal made it 2-0 and effectively ended Angers' hopes of recovering a result.
Tolisso's contribution capped an impressive afternoon for the Lyon captain, who also played a role in creating Nuamah's opening goal.
Lyon climb into the top three
The victory was important for Lyon as they look to remain involved in the Ligue 1 title race and secure European football for next season.
With 17 points from nine matches, Fonseca's team moved into third position, level on points with fourth-placed Paris FC but ahead on goal difference.
Lyon will now turn their attention to their upcoming European assignment against Real Sociedad as they look to maintain their positive momentum.
For Angers, the defeat represents another difficult result as they continue their campaign in the French top flight.