Pereira was taking charge of Forest for the first time after he became their fourth manager of a chaotic season and it could not have gone better as they took a decisive lead in the play-off round first leg in Istanbul.
Goals from Murillo, Igor Jesus and Morgan Gibbs-White made it a memorable night for Forest as life after Sean Dyche, Ange Postecoglou and Nuno Espirito Santo began in freescoring fashion.
The victory means, barring a disaster in next week's second leg at the City Ground, Forest will earn a last-16 tie against Real Betis or Midtjylland.
Pereira's main brief in his new role is to ensure Forest retain their Premier League status and this performance should give confidence going into Sunday's home game with Liverpool.
In perhaps a veiled dig at Dyche, skipper Gibbs-White said on TNT Sports: "I felt like we had a real identity out there today.
"I think his message to us is that we're going to have a real identity of how we play and how we defend as a team.
"I feel like him and his staff have brought a real positive energy into the group and we've all bought into what he wants straight away."
"And I think that's the most important thing, buying into each other and understanding each other.
In some of the other first-leg action, Celtic were thrashed 4-1 at home by Stuttgart, Panathinakos and Viktoria Plzeh drew 2-2, Ludogorets defeated Ferencvaros 2-1, Celta Vigo beat PAOK 2-1 away, Bologna won 1-0 at Brann and Genk whipped Dinamo Zagreb 3-1 away.
In the Conference League, Crystal Palace's hopes hang in the balance after a 1-1 draw at Bosnian Premier League side Zrinjski Mostar in the first leg of their knockout phase play-off.
Oliver Glasner had reinforced his attacking ranks since their last European outing in December, but it was Ismaila Sarr, assisted by January signing Jorgen Strand Larsen, who broke the deadlock on the stroke of half-time.
The Eagles allowed Karlo Abramovic to score a second-half equaliser, then failed to create many chances, coming closest when Adam Wharton rattled the crossbar.
It was another disappointing display from the struggling Premier League side, once touted as favourites to win the competition, but now hoping they can simply turn around a more inspiring outing at Selhurst Park and survive beyond next week.
In some of the other results, Armenia's Noah surprised Dutch side AZ Alkmaar 1-0 courtesy of Hovhannes Hambardzumyan's 53rd minute winner.
Czech club Sigma Olomouc drew 1-1 with Switzerland's Lausanne, Poland's Lech Poznan won 2-0 in Finland at Kuopion while Fiorentina won 3-0 at Jagiellonia Bialystok 3-0.
The return legs are next Thursday.
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