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Two late goals against Bournemouth finally gave Frank Lampard his first win since his return as Chelsea's interim manager.
The Blues had lost all four Premier League games since Lampard's return in April, but had led through Conor Gallagher's early header.
Matias Vina levelled for Bournemouth, but Benoit Badiashile and Joao Felix struck inside the last 10 minutes.
Relegation remains a possibility for the Cherries with three games left, while Chelsea are 11th in the table.
Bournemouth's best spell came early in the second half when Vina missed a chance for a second and Dango Ouattara headed over from close range, but Gary O'Neil's side still have a good chance of avoiding a quick return to the Championship with games against Crystal Palace, Manchester United and Everton to come.
They are currently nine points clear of the bottom three, although some teams still have four matches to play.
With Pierre-Emerick Aubameyang and Raheem Sterling among five players left out from the side that had lost 3-1 at Arsenal in their previous outing, Chelsea were much improved with 21-year-old Noni Madueke a particular threat on the right-hand side.
Lampard had opted to bring in Gallagher as well as Badiashile, Trevoh Chalobah, Mykhailo Mudryk and Kai Havertz, and he said shaping a side from a large squad after a poor run has been difficult.
"There are a few players finding their feet," Lampard said.
"Typically at Chelsea, one or two have fed into the group and now we have more. It's understandable that as a group finding rhythm and confidence can be difficult.
"This is a first step, it won't be plain sailing but there is talent there and the players need to come together to get us to where we want to be.
"We came in off the back of a tough run, it's been a tough year and there is a lot work to do. But the performance and the result in isolation are really good, we deserved to win the game. It's a nice step forward for the lads."
Chelsea's recent record made for grim reading, with defeats to Real Madrid in both legs of their Champions League quarter-final to go alongside the losses in the league and just two goals scored in those six outings under Lampard.
But Lampard's tweaks to the side that had gone 3-0 behind after just 34 minutes against Arsenal paid off, with Gallagher looking lively throughout after his deft, glancing header diverted N'Golo Kante's fine cross from the right in the ninth minute.
Madueke found the side netting in the first half, as well as posing problems for Bournemouth when cutting inside from the left with some fine runs.
Badiashile, another of Lampard's changes from midweek, also impressed in giving Chelsea a much more solid feel at the back and he thoroughly deserved his first goal since his arrival from Monaco in January with a poke from close range to Hatem Ziyech's free-kick.
Felix finished off a cute exchange of passes with Sterling, on as a substitute in the second half, to give a comfortable-looking gloss to the scoreline.
But even after the relief of his first win, Lampard knows he still faces a tricky end to the season.
Chelsea face relegation-threatened Nottingham Forest next, before a daunting final trio of games against clubs currently in the positions Chelsea fans would expect to be contesting: Manchester City, Manchester United and Newcastle United.
Thomas Tuchel was still Chelsea's manager when Gary O'Neil replaced Scott Parker in late August in the wake of the Cherries' disastrous 9-0 loss at Liverpool, but while the German lasted only just over a week more, O'Neil has repaid the faith shown in him despite some dips in form since his appointment.
A run of six wins in nine games prior to Chelsea's visit has lifted Bournemouth from the very foot of the table in early March to the cusp of safety, and even this defeat still leaves them nine points clear of Leicester, Leeds and Forest below them.
Astute business in January has been key to their revival under O'Neil with Vina, on loan from AS Roma, grabbing his second goal inside a month after an excellent move that also involved the impressive Ryan Christie.
Cutting in from the left and quickly exchanging passes with Christie and Dominic Solanke, Vina then opened up his body and curled the ball high past Kepa Arrizabalaga for a brilliant equaliser.
Vina should arguably have had another in the second half, but Kepa was equal to the Uruguay international's near-post shot to his right.
Ouattara, who had also arrived in January on a permanent deal from Lorient, should have hit the target with his header from inside the six-yard area and the impressive Burkina Faso midfielder's miss proved vital when Chelsea subsequently stretched away.
