Nicolas Jackson has scored in three successive Premier League games for the first time
Nottingham Forest missed the chance to secure Premier League safety after losing to Chelsea in a five-goal thriller at the City Ground.
A resurgent Chelsea took the lead through their first attack when Mykhailo Mudryk swept home in the eighth minute after a beautifully crafted pass by Cole Palmer.
But after Willy Boly headed Forest level, former Chelsea winger Callum Hudson-Odoi sent Forest into a 74th-minute lead with a curling finish from 15 yards.
In an entertaining encounter, substitute Raheem Sterling made it 2-2 before Nicolas Jackson struck an 82nd-minute winner.
Luton's defeat at West Ham earlier on Saturday meant Forest required one point to confirm a third successive season in the Premier League.
Nuno Espirito Santo's side have 29 points from 37 games, three more than 18th-placed Luton who also have one match left.
However, Forest also have a superior goal difference, with Luton requiring a 12-goal swing to stay up.
The Reds go to relegated Burnley on the final day on 19 May, while Luton host Fulham.
Forest's missed opportunity
Forest have a good foundation to build on - Nuno
There were mixed emotions at full-time as Forest missed the chance to make mathematically certain of their place in the Premier League next season.
Instead it will go down to the final day, although it will require a highly unlikely set of circumstances for Forest to go down.
While they have a goal difference of -19, Luton - who must win to draw level with them on points - are on -31.
Nuno and his players walked around the pitch applauding their fans in a show of appreciation after their final home game of the season.
But deep down they will feel this was an opportunity missed, conceding two late goals as Chelsea secured a first Premier League away win since 12 February.
"We knew it was in our hands to achieve the main objective to stay in the Premier League," Nuno told BBC Sport.
"It's not yet done but the way the players stuck to their task, we are positive for the next one to finally finish the job.
"The fans show us what it means. They have been so supportive. We are disappointed because they deserve a moment of happiness."
It has been a difficult season with the loss of Brennan Johnson, the sacking of Steve Cooper as well as the four-point punishment for breaching Premier League profit and sustainability rules.
But barring an extraordinary final day, Forest will be back in the top tier next season.
Chelsea's end-of-season resurgence
Pochettino delight at Chelsea's 'important victory'
Chelsea will not want the season to end.
Mauricio Pochettino's side are enjoying a resurgent end to a difficult campaign, with the mood around the club transformed following wins over Tottenham, West Ham and now Forest.
There were more positives for Pochettino to take into next season as Nicolas Jackson scored for the fourth time in his past three league games, while Reece James marked his first appearance since December with the assist for the winner.
Whether Pochettino is still at Stamford Bridge next season is still to be determined.
The Argentine said on the eve of the match that he and his coaching staff must have the full backing of the owners and "it will not be the end of the world" if the two parties end up going their separate ways.
There will be many Chelsea fans who hope he stays.
Having spent much of the season loitering around mid-table, they enter the final week level on 57 points with sixth-placed Newcastle and with playing in Europe next season a possibility.
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