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After four consecutive Clasico defeats, Barcelona claimed their first triumph over Real since March 2023.
Iniesta, 40, was at the heart of the Spain and Barcelona midfield during a period of sustained success for both teams in the late 2000s and early 2010s.
Flick, who has not managed a club since being sacked by Germany in September, 2023, will be tasked with reviving Barcelona's fortunes after the Catalan side failed to win any trophies this season under Xavi Hernandez.
The decision ended months of arguments between Barca and Xavi who made 767 appearances as a midfielder for the Spanish giants and helped them win 25 major trophies.
Bonhams said the auction was on behalf of Horacio Gaggioli, an agent from Messi's home country of Argentina, who was part of the deal.
Goals from Brahim Diaz, Jude Bellingham and Joselu earned Real a 3-0 win over lowly Cadiz. Later, Girona beat Barcelona 4-2, a result that left Carlo Ancelotti's side with an unassailable lead in the standings.
The result left second-placed Barca 11 points adrift of the leaders with six games left.
PSG will face Borussia Dortmund in the semifinals after the Germans beat Atletico Madrid.
PSG came into the match unbeaten in their last 27 games in all competitions but were undone by a fired-up Barcelona side looking to return the club to the summit of European football.
Arsenal survived a penalty shootout to scrape past Porto and reach the quarter-finals of the Champions League for the first time in 14 years.
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