In other matches, super-sub Messi helped Barca romp past Atletico
Barcelona followed up Saturday's win over Real Madrid with another victory when Alexis Sanchez set the champions on their way to a 3-0 success at Celta Vigo on Tuesday that put them four points clear at the top of La Liga.
Real Madrid got their LaLiga title defence off to a limp start as they were held to a 1-1 draw at Mallorca.
Real Madrid signed Mbappe as a free agent in a five-year deal after the Frenchman's contract expired at Paris Saint Germain (PSG).
La Liga players dominate this year's Best Player in Europe shortlist, announced by the continent's governing body UEFA on Monday, with seven of the top 10 contenders for the prestigious award currently plying their trade in Spain.
"We are really pleased and we just have to enjoy it," Celta defender Gustavo Cabral told Spanish television.
A summary of Tuesday's Champions League Round of 16, Second Leg, matches.
Lionel Messi created a goal and scored another as Barcelona came from behind to beat struggling Rayo Vallecano 3-1 at home on Saturday and stay seven points clear at the top of La Liga.
The win took second-placed Real to 62 points after 29 games, two behind champions Barca who beat Leganes 2-0 on Tuesday.
Beat Real Madrid's unbeaten run in the 1988-89 season, and thump Rayo Vallecano 5-1
'I have no regrets, I wouldn't change a thing.'
Barcelona's bid for a fifth La Liga title in six years suffered a surprise setback when the champions crashed to a 1-0 defeat at lowly Real Valladolid on Saturday.
Atletico Madrid made a typically aggressive start to lay the foundations for a 2-0 victory at home.
Gareth Bale marked his return to action after a long injury layoff by sealing a 2-0 victory for Real Madrid over Espanyol on Saturday to provisionally stretch Zinedine Zidane's side's lead at the top of La Liga to three points.
Atletico Madrid's La Liga title challenge took a nosedive when they slumped to a shock 3-0 defeat at Osasuna on Sunday, leaving Real Madrid three points clear at the top.
Robert Lewandowski smashed home a rebound to earn Barcelona a 2-1 win against Athletic Bilbao in an absorbing LaLiga clash on Saturday.
Karim Benzema netted a second-half hat-trick as Real Madrid got back to winning ways with a 3-0 victory over Athletic Bilbao in La Liga on Sunday.
At $16.8 million per match, the IPL is only behind America's National Football League.
Atletico Madrid's Brazil-born forward Diego Costa has signed a formal letter stating his wish to play for adopted country Spain, ending a tug-of-war between the two powerhouses over the in-form 25-year-old.
Real Madrid tightened their grip on top spot by beating Alaves 3-0 at home in La Liga on Sunday to provisionally move five points ahead of nearest challengers Barcelona despite coach Zinedine Zidane making a string of changes in defence.
Casemiro headed an 89th minute winner to earn Real Madrid a barely deserved 2-1 victory at Las Palmas in La Liga on Sunday as they closed the gap on second-placed Atletico Madrid to four points.
Villarreal continued their impressive revival after a season in the second division when Jeremy Perbet and Jonathan Pereira struck in a 2-1 win at home to Espanyol in La Liga on Thursday.
Villarreal tightened their grip on fourth place in La Liga when Nigerian forward Ikechukwu Uche's last-gasp strike snatched a 1-0 win at fellow promoted side Elche on Monday.
A towering Diego Godin header secured Atletico Madrid a 1-1 draw against Barcelona and a first La Liga title for 18 years in a thrilling climax to the campaign on Saturday.
Real Madrid beat Leganes 4-2 on Wednesday despite resting key players including Cristiano Ronaldo and Gareth Bale as goals from Alvaro Morata and James Rodriguez helped them stay top of La Liga after Barcelona cruised to a 3-0 win over Sevilla.
The home side spurned two chances to extend their advantage before the break but Barca levelled in the 52nd minute when Luis Suarez glanced in Lionel Messi's free kick.
Barcelona, Las Palmas match postponed over Catalan referendum
Leeds reach Championship play-offs final with 4-0 win over Norwich
The Ballon d'Or, which is awarded annually since 1956, is one of the most prestigious individual honours in football.
Manchester City squandered a three-goal lead to draw 3-3 with Feyenoord in the Champions League on Tuesday.
Sporting marked the final home game of coach Ruben Amorim's reign in stunning fashion as Viktor Gyokeres' hat-trick saw them come from behind to thrash Manchester City 4-1 and maintain their superb start to the Champions League on Tuesday.
Valencia lost ground in the battle with Atletico Madrid and Sevilla for third place in La Liga when they conceded a late Aritz Aduriz equaliser in a bad-tempered 1-1 draw at Athletic Bilbao on Thursday.
Real Madrid's hopes of overhauling La Liga leaders Barcelona suffered a stinging blow when they were held to a 2-2 draw at home to Valencia.
Barcelona top the LaLiga standings with 15 points, four ahead of Real Madrid and Villarreal. Girona are seventh on seven points.
La Liga champions Barcelona's domestic struggles continued as they dropped points for the third game in a row, drawing 1-1 at home to Athletic Bilbao on Saturday after Lionel Messi and Sergio Busquets had begun the match on the substitutes' bench.
Jaume Costa atoned for giving away a first-half penalty when his strike five minutes from time rescued Villarreal a 1-1 draw against Eibar that put them fourth in La Liga on Sunday.
Key head-to-head battles in Saturday's "Clasico" between Real Madrid and Barcelona at the Bernabeu stadium (1600 GMT)
A round-up of Saturday's football action in La Liga, Bundesliga and Ligue 1.
Rishabh Pant has been nominated for the prestigious Laureus World Comeback of the Year Award.
Barcelona's Lionel Messi hit his 400th career goal for the La Liga leaders.