The Magpies had fallen behind when Sven Botman gifted Emmanuel Dennis the opening goal on 26 minutes.
But Isak levelled for Eddie Howe's men and ended Forest's nine-game unbeaten home league run stretching back to September with a cool spot-kick after Moussa Niakhate handled inside his own area.
Defeat leaves Forest still two points above the relegation zone, but they deserved little more after being outplayed from start to finish.
Newcastle ended a near two-month wait for a Premier League win last weekend in beating Wolves but back-to-back victories has put them right back in the race for Champions League football next season.
The closest the visitors came to turning their early dominance into a lead was when Renan Lodi turned Isak's cross onto his own crossbar.
Instead it was Forest who went in front completely against the run of play thanks to a howler from Botman.
The Dutch centre-back has been a major factor in Newcastle's success this season but his attempted pass back to goalkeeper Nick Pope was intercepted by Dennis, who produced a stunning chipped finish beyond Pope and Kieran Tripper for just his second Forest goal.
The crossbar came to the home side's rescue again when Sean Longstaff's deflected strike from the edge of the box came back off the woodwork.
Newcastle finally got their reward in first half stoppage time when the club's record signing Isak acrobatically flicked in Joe Willock's cross off the post.
The pattern of play continued after the break as the Magpies laid siege to the Forest goal.
Former Real Madrid and Paris Saint-Germain goalkeeper Keylor Navas had to be at his best to turn over powerful drives from Elliot Anderson and Bruno Guimaraes.
Anderson then thought he had his first senior goal when he headed in Isak's cross at the back post.
However, the goal was controversially disallowed after a VAR check for offside against Longstaff in the build-up despite the ball breaking to the midfielder off a Forest player.
Chances continued to come and go for the visitors as Willock fired a glorious chance wide before Serge Aurier cleared off the line from Isak.
Forest could still have stolen all three points when Pope's outstretched leg denied Brennan Johnson a winner four minutes from time.
But just when they looked set to hold out for a precious point in their battle to beat the drop, Niakhate needlessly put his hand up to block Isak's tame header.
The Swedish international's debut season in England has been blighted by injury, but he showed his class by keeping his head to slot past Navas and spark wild scenes of celebration among the away support.
اخلاء مسئولية! : هذا المحتوى لم يتم انشائة او استضافته بواسطة موقع اخبار الكورة و اي مسؤلية قانونية تقع على عاتق الموقع مصدر الخبر : بي ان الرياضية  , يتم جمع الاخبار عن طريق خدمة ال RSS المتاحة مجانا للجمهور من المصدر : بي ان الرياضية  مع الحفظ على حقوق الملكية الخاصة بمصدر الخبر.