Luis Suarez scored the winner in the 89th minute in front of nearly 99,000 people, who packed the stands to see new signings Antoine Griezmann and Frenkie De Jong.
Antoine Griezmann's 120 million-euro transfer was contested by Atletico Madrid, who insisted Barcelona should have paid a higher price for the World Cup-winning French striker.
Antoine Griezmann was presented as a Barcelona player on Sunday night, after Barcelona paid the 28-year-old's 120-million-euro ($135 million) release clause.
Antoine Griezmann joined Atletico Madrid in 2014 and scored 133 goals in 257 appearances, lifting the Europa League in 2018.
Antoine Griezmann was unable to add to his tally of 133 goals in 257 games across all competitions in what became a bitter end to his five successful seasons for Atletico Madrid.
With 133 goals in 252 games at Atletico Madrid, Antoine Griezmann has been ever-present and has rarely been unfit or injured.
Raheem Sterling's hat-trick saw England start their Euro 2020 qualifying campaign by hammering the Czech Republic 5-0.
Antoine Griezmann surpassed Fernando Torres with his 130th goal for Atletico Madrid.
Real Madrid's fifth league win in a row means they sit second in La Liga for the first time since September, above Atletico Madrid.
Antoine Griezmann now has eight goals in as many games, his latest helping Atletico register their sixth win in seven league matches.
Atletico Madrid had 19 shots and, unusually for them, dominated possession.
Luka Modric won the 2018 Ballon d'Or, Cristiano Ronaldo was second, with France and Atletico Madrid striker Antoine Griezmann completing the podium.
Loew insisted he was "very pleased" with the performance as Germany were much improved compared to the team that lost 3-0 against the Netherlands.
Antoine Griezmann is one of the most accomplished strikers in European football.
Sergio Ramos has launched a scathing attack on Antoine Griezmann's attitude after the French forward said he is on a par with Lionel Messi and Cristiano Ronaldo.
Ballon d'Or has been won by Cristiano Ronaldo and Lionel Messi a record five times apiece.
France were held to a 0-0 draw by Germany in Munich in a flat start to the new UEFA Nations League.
Antoine Griezmann insists he deserves to be on the podium for this year's Ballon d'Or after winning the World Cup and major silverware with Atletico Madrid.