Morgan Gibbs-White, Neco Williams and Jota Silva were also on target after Lewis Dunk's own goal opened the scoring in an astonishing performance from Nuno Espirito Santo's men as they bounced back from a 5-0 defeat at Bournemouth last weekend.
Victory takes Forest level on points with second-placed Arsenal and opens up a seven-point cushion on sixth-placed Chelsea. Fifth place in the Premier League this season is almost certain to be enough for Champions League qualification due to a strong start by English clubs in European competitions.
Two-time European Cup winners in 1979 and 1980 during the club's heyday under Brian Clough, Forest last played in Europe back in 1996. But a run of 10 wins from their last 12 games has put them well on course to end that two-decade wait for continental competition.