The Frenchman had only been on the pitch for a few minutes when he came up with the telling moment thanks to an assist from debutant Jadon Sancho, as Andoni Iraola's men were left to lament their wastefulness throughout the evening.
The hosts huffed and puffed but could not blow Chelsea's defences down, although Nkunku was blowing his blue balloon after sending the away end into raptures at the end of a bad-tempered clash, where 14 yellow cards - a record for a single Premier League fixture - were dished out by Anthony Taylor.
Rather than pick the Cherries off, Chelsea had their backs pinned against the wall by their South Coast hosts, who gave the Blues a huge scare in the opening few minutes as Marcus Tavernier crashed a terrific effort against the bar.
Enzo Maresca's pacy men still offered some threat in the final third, but not to the level of troubling stand-in goalkeeper Mark Travers - deputising for the ineligible Kepa Arrizabalaga, whose former Chelsea rival Robert Sanchez was briefly the villain before making amends straight away.
The Spaniard felled Evanilson inside the area but produced a top save from the Brazilian's penalty to keep Chelsea on terms heading into the break, and he was called into action several more times as black and red shirts continued to surge forward.
The killer product was just not there for the hosts, though, but Sancho and Nkunku had the recipe for attacking success in the 86th minute, as Chelsea made it two wins from as many away matches in the 2024-25 season.
At the conclusion of a fiery affair, Maresca's men are up to seventh, while the Cherries are 11th on account of their first loss of the season, albeit an unwarranted one.
BOURNEMOUTH VS. CHELSEA HIGHLIGHTS
Robert Sanchez penalty save vs. Bournemouth (38th min, Bournemouth 0-0 Chelsea)
From zero to hero in the space of a couple of minutes! Bournemouth had been banging on the Chelsea door throughout the first half and were seemingly set to draw first blood when Evanilson was brought down in the box by Sanchez.
The Cherries striker stepped up to take the spot kick and certainly did not do much wrong from 12 yards, but Sanchez brilliantly sprung to his left and kept out Evanilson's low spot kick.
Immediate redemption for the Spaniard, and a penny for Kepa's thoughts in the stands!
Evanilson disallowed goal vs. Chelsea (53rd min, Bournemouth 0-0 Chelsea)
Certainly not Evanilson's night so far! The former Porto man heads a cross into the bottom corner, but Chelsea had already stopped due to the offside flag, and the South American's goal is indeed chalked off.
Christopher Nkunku goal vs. Bournemouth (86th min, Bournemouth 0-1 Chelsea)
The balloon is out, the Blues are bouncing, and the Cherries are crestfallen! Two of Maresca's substitutes combine for what will surely be an arguably undeserved winning goal for the visitors.
Sancho has been excellent on his debut and picks a smart pass into the feet of Nkunku, who produces a slick turn and remarkably out-muscles Ilya Zabarnyi before poking the ball into the far corner!
MAN OF THE MATCH - ROBERT SANCHEZ
All should have been forgiven when Sanchez immediately atoned for giving the penalty away by saving said penalty; the Spaniard may have guessed correctly, but it was still a challenging save to make, as Evanilson's spot kick was bound for the bottom corner.
The 26-year-old continued to excel in between the posts all night long, racking up seven stops in total and helping to take the sting out of Bournemouth's desperate attacks right towards the end, confidently catching an injury-time corner among a sea of bodies before parrying away one final Enes Unal effort. Number one spot secured.
BOURNEMOUTH VS. CHELSEA MATCH STATS
Possession: Bournemouth 33%-67% Chelsea
Shots: Bournemouth 19-10 Chelsea
Shots on target: Bournemouth 7-3 Chelsea
Corners: Bournemouth 6-3 Chelsea
Fouls: Bournemouth 16-9 Chelsea
BEST STATS
WHAT NEXT?
Bournemouth have a huge challenge on their hands to make an instant return to winning ways, as the Cherries head to Liverpool next Saturday, while Chelsea face London rivals West Ham United away from home in the lunchtime kickoff.