Only Danilo survived from the Forest team that thrashed Brighton and Hove Albion 7-0 last week, while Exeter made five changes as defenders MacDonald and Turns made their debuts after last week's 4-1 loss at Stevenage.
Exeter caught Forest cold when goalkeeper Carlos Miguel fumbled Demetri Mitchell's curling effort into the path of Josh Magennis to score the opener from close range after just five minutes.
But Forest soon found their stride as Taiwo Awoniyi went close twice – the second needing a fine goalline clearance from Vincent Harper – before Ramon Sosa levelled as he coolly finished from Ibrahim Sangare's weighted pass.
Awoniyi had 32nd-minute shot well saved by Exeter keeper Joe Whitworth before he deservedly put Forest ahead soon after as he fired into the bottom corner after turning well on the edge of the box as Turns and MacDonald struggled to contain the Nigerian striker.
However, Magennis restored Exeter's lead five minutes after the restart, this time on hand to score a deflected effort after a scramble from a deep corner.
Miguel was forced off with an injury soon after, with keeper Mats Sels replacing him.
Sels had to be alert to palm away an Ilmari Niskanen strike five minutes later as a rejuvenated Grecians – backed by a vociferous home end of packed fans – had their best spell of the game.
Forest brought on Elliot Anderson and Gibbs-White with 20 minutes left and the pair both went close as the top flight side shifted up a gear.
Exeter gave Forest another scare as they pressured late on with a series of corners – one effort needing a desperate block from defender Willy-Arnaud Boly to clear the danger.