England international Morgan Gibbs-White and the in-form Chris Wood struck before half-time to take Forest to within six points of leaders Liverpool, who they host in their next Premier League game.
Substitute Taiwo Awoniyi rounded off the scoring and a sixth consecutive win for Forest in stoppage time.
Defeat leaves Wolves outside the relegation zone only thanks to goal difference as they suffered a first defeat under new boss Vitor Pereira.
Forest remain third in the table but move level on points with Arsenal.
Even if a shock title challenge proves beyond Espirito Santo's men, they are building up an impressive cushion in the race for Champions League football next season.
They are five points clear of fifth-placed Newcastle and six in front of struggling champions Manchester City in sixth.
A top-four finish would guarantee a return to the continent's elite competition for the first time in 45 years for the two-time European champions.
However, fifth could also be good enough depending on how English club fare in European competition this season.
"We need to stay humble. We haven't achieved anything yet, we need to work until the end and this can lead us to good moments," said Espirito Santo.
Gibbs-White savoured his return to the club where he spent the early part of his career.
In front of the watching new England manager Thomas Tuchel, the midfielder did his case for further international recognition no harm with a cool finish from Antony Elanga's pass.
Forest's unexpected rise from battling relegation until the final day of last season into Champions League contenders has been build on a solid defence and Wood's purple patch.
The New Zealand international turned in Callum Hudson-Odoi's low cross for his 12th goal of the season to double the visitors' lead just before half-time.
Wolves pressed and probed for a way back into the game after the break but were toothless in the absence of talisman Matheus Cunha through suspension.
Mats Sels was forced into one brilliant save to deny Jorgen Strand Larsen to preserve a ninth clean sheet of the season and fourth in a row.
That solidity is familiar to Wolves fans from Espirito Santo's time in charge of their club between 2017 and 2021.
The Portuguese coach led Wanderers from the Championship into Europe for the first time in 39 years.
Now after troubled spells at Tottenham and Saudi club Al-Ittihad, he is recreating that magic to leave Forest fans in dreamland.
"As coaching staff we have this natural ambition of improving the players, this is what we are obsessed with," he added.
"If we improve the players then the team will improve and if the team improves then the club will improve and the city will be happy."
