The visitors' pressure eventually paid off when Willock set-up Isak for a precise volley into the far corner on the stroke of half-time and the Swedish striker later delivered the winner to spark celebratory scenes in the away end in Nottingham.
The result leaves Newcastle just a point behind Tottenham in fifth - and still with a game in hand - while Forest remain two points above the relegation zone.
Newcastle's effort pays off as Forest woes continue
Newcastle were made to work hard for their victory but it was well deserved.
They had already forced Forest goalkeeper Keylor Navas into action on numerous occasions in the second half as pressure grew inside the hosts' half, while defender Serge Aurier made a goalline clearance and striker Jacob Murphy volleyed wide from close range.