The Championship side, who are currently sitting in the relegation zone, pulled off a stunning 4-1 victory over Steve Cooper's side to dump the Premier League team out of the competition.
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Goals from Marvin Ekpiteta, Ian Poveda, CJ Hamilton and Jerry Yates were enough to see the Tangerines to a shock victory that sees them earn a place in the fourth round and sends Forest crashing out.
Chesterfield were painfully close to pulling off a major shock of their own as the National League side were denied a win over West Brom as they played out a 3-3 draw, teeing up a replay at The Hawthorns.
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Premier League side Bournemouth were also knocked out of the competition by recently-relegated Burnley.
Vincent Kompany's side earned a 4-2 victory at the Vitality Stadium thanks to braces from Manuel Benson and Anass Zaroury to send the Championship high-flyers through to the next round.
Elsewhere, League One side Fleetwood knocked QPR out of the competition with a 1-0 victory while Watford were knocked out by Reading thanks to a 2-0 defeat.
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Elsewhere, Leicester, Tottenham, Southampton, Fulham and Brighton all secured a spot in the fourth round as they represent the Premier League in the competition, while Sunderland managed a late comeback to avoid elimination at the hands of Shrewsbury.