Real Madrid suffered a 3-2 defeat by Villarreal in La Liga on Saturday in a thrilling clash ahead of their Champions League showdown against Chelsea next week.
Real Sociedad beat Getafe 2-0 to tighten their grip on fourth place, while Villarreal rose to fifth after their impressive triumph at the Santiago Bernabeu.
Pau Torres's own goal sent Madrid in front but Chukwueze levelled before the break.
Vinicius Junior netted a superb solo goal before Jose Luis Morales equalised again and Chukwueze curled home a superb winner, which reduced Madrid's hopes of retaining the title to virtually nothing.
"The truth is, it was hard for us to be 100 percent motivated, that's quite normal," Real Madrid coach Carlo Ancelotti told Movistar.
"If you aren't 100 percent, you have to be better on the pitch, we weren't organised, they manage the ball well and it was hard for us to get it back."
However the coach said the defeat did not allow any doubts to creep in ahead of Chelsea's visit in the Champions League quarter-final first leg.
"We knew it could be complicated, and Wednesday is another story. Our level dipped a bit today, but on Wednesday it will be at the maximum."
The coach made six changes from the 4-0 Clasico thrashing of Barcelona in the Copa del Rey semi-final midweek, with Europe in mind.
However he maintained his attacking trio of Karim Benzema, Rodrygo and Vinicius, looking to put the game to bed early.
Marco Asensio and Vinicius combined for Madrid's opener, with Torres deflecting the latter's cross into his own net.
The visitors levelled late in the first half when Chukwueze's magical footwork left defender Nacho Fernandez for dead, and the Nigerian finished clinically past Thibaut Courtois.
Madrid came out flying in the second half and Vinicius scored a brilliant goal of his own, nutmegging defender Aissa Mandi to leave a crowd of perusers behind him, before slipping the ball home.
The Brazilian winger, on 21 goals across all competitions, should have matched his tally of 22 last season but fired into the side netting after being teed up by Benzema.
The French forward, who scored hat-tricks in both his previous two games, was withdrawn before the hour mark to rest him for the Chelsea clash.
- Stunning comeback -
Villarreal pulled themselves level in the 70th minute when Chukwueze's cross caused danger and substitute Morales finished well.
With 10 minutes remaining, Chukwueze scored a brilliant second, curling into the top corner from outside the area.
It was his fifth goal in his last seven La Liga matches, with Chukwueze in the best form of his career to date.
Madrid were awarded a late penalty when the ball appeared to strike Mandi's arm as he slid along the floor, but VAR showed there was no offence committed.
"The league is complicated, that's obvious, but we're alive in two other competitions that we will try to win," said Madrid defender Lucas Vazquez.
Villarreal rose to fifth, two points clear of Real Betis, who host Cadiz on Sunday.
Coach Quique Setien lavished praise on Chukwueze.
"For a few weeks he's been giving us a lot, he's a permanent threat," said the former Barcelona boss.
"Not just in goals, but in passes, chances, he's an extraordinary player who is giving us a lot."
- La Real improve -
Mikel Oyarzabal and Takefusa Kubo struck for Real Sociedad in their comfortable win over Getafe.
Amid a run of inconsistent form after a strong start to the season, La Real suffered Europa League elimination and in recent weeks allowed teams to close in behind them in the hunt for Champions League football.
Atletico Madrid, third, overtook Real Sociedad in March after they dropped points in a draw with lowly Cadiz.
With this solid victory, Real Sociedad are four points clear of Villarreal and six ahead of Betis.
Earlier Athletic Bilbao bounced back from their Copa del Rey semi-final defeat by Osasuna this week with a 2-1 win over Espanyol.
Barcelona winger Ez Abde, on loan at Osasuna, shone and struck twice for the cup finalists in a 2-1 win over bottom of the table Elche.