Goals from Mykhailo Mudryk, Raheem Sterling, and Nicolas Jackson secured a third consecutive win for Mauricio Pochettino's side, pulling them level with sixth-placed Newcastle with two games remaining.
Pochettino, whose future at the club hangs in the balance, could potentially guide the Blues to either the Europa League or Europa Conference League, depending on Manchester United's final league position and FA Cup outcome.
Despite goals from Willy Boly and Callum Hudson-Odoi giving Forest a 2-1 lead, their Premier League safety remains almost assured. They sit three points above 18th-placed Luton Town and possess a superior goal difference, making relegation highly unlikely on the final day.
Given their four-point deduction for breaching Premier League financial rules and their grievances with refereeing decisions this season, Nottingham Forest view survival as a defiant response to the Premier League.
Forest owner Evangelos Marinakis is likely delighted with the week's events, having witnessed his other club Olympiacos reach their first-ever European final by defeating Aston Villa in the Europa Conference League semi-final.
With losses for Burnley and Luton earlier in the day, there was a celebratory atmosphere at the City Ground. Despite their near-certain safety, Forest fans expressed their discontent with the season's challenges by booing the Premier League anthem and displaying a banner reading, "When they try to keep us down, we show them who they are."
However, Chelsea played the role of party poopers, taking the lead in the eighth minute through a goal from Mykhailo Mudryk, assisted by Cole Palmer's incisive pass.
Forest responded well, equalizing eight minutes later when Willy Boly headed in a free-kick with the aid of a deflection.
In their quest for the three points needed to secure safety, Forest hit the woodwork twice in the opening 15 minutes of the second half. Ryan Yates and Morgan Gibbs-White both came close, with Chris Wood missing a golden opportunity from close range.
Thiago Silva hit the post for Chelsea before Forest struck the woodwork again when Callum Hudson-Odoi's shot deflected onto the crossbar.
Hudson-Odoi then put Forest ahead in the 74th minute with a precise finish, but Chelsea responded with two quick goals from Raheem Sterling and Nicolas Jackson, securing victory for the visitors.