Eddie Howe’s side trailed at half-time through Murillo’s header but turned the game around in second interval with Alexander Isak, Joelinton and substitute Harvey Barnes finding the net.
The win saw Newcastle move up to eighth in the league table, one point behind Forest in third.
Howe named an unchanged starting XI from last weekend’s 1-0 win over Arsenal at St James’ Park.
United started brightly but fell behind in the 21st minute when Murillo headed home Anthony Elanga’s free-kick delivery. It came after Joe Willock was penalised for fouling Elanga from a corner that was incorrectly awarded.
The Magpies had 60% possession when the half-time whistle blew but couldn’t find a breakthrough. Dan Burn and Bruno Guimaraes both had efforts that were saved by Forest goalkeeper Matz Sels.
United equalised in the 54th minute and it came via an unlikely source... a corner. Anthony Gordon’s in-swinging delivery hit off Chris Wood and Isak reacted quickest to prod the ball home.
It was the first corner Howe’s side have scored from since Fabian Schar’s goal against Tottenham Hotspur in April.
Joelinton then put the visitors in front when he cut inside on his left foot to fire the ball into the bottom corner. Barnes then wrapped up the three points inside the remaining 10 minutes.
Here’s our Newcastle United player ratings:
1. GettyImages-2184003681
Getty Images
2. Nick Pope - 7
Felt aggrieved after a clear goal-kick was awarded as a corner just before Murillo’s opener. Made a smart stop with his foot to deny Nicolas Dominquez at 1-0. | Getty Images
3. Tino Livramento - 7
Made several overlapping runs and although he lacked a final ball showed a fantastic engine. | Getty Images
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4. Fabian Schar - 7
Newcastle had Forest penned in but a misplaced pass allowed the hosts to get up field and eventually open the scoring. Improved after the break like his teammates. | Getty Images