After their 1-1 draw at the Santiago Bernabeu, Spurs extended their unbeaten start in the Champions League and left both sides level on seven points in Group H.
An own goal courtesy of Raphael Varane put the visitors ahead in Madrid, but Real equalised from the spot through Cristiano Ronaldo just before half-time.
When the two sides meet again in two weeks, the clash will potentially decide who finishes top of the group, and Balague believes the North London club have proved they can compete at the very top level.
"They were not in awe of the Santiago Bernabeu, they were not in awe of Real Madrid," said the 'Sky Sports' columnist.
"After Chelsea beat Atletico Madrid, it wasn't a victory by accident, Diego Simeone said they were outstanding, and it was the way they were outstanding.
"Chelsea controlled the game and knew what tempo the game deserved. With Spurs it was exactly the same.
"They knew what they had to do. It was about personality, it was about the tactics of the group.
"Even Pochettino said in the press conference, the draw was good, but it's about competing and showing they're at the level of these guys, and I think they are.
"English sides are doing exactly that, so we could be seeing the end of the Spanish domination."
Before the game, most of the talk was about in-form Spurs striker Harry Kane, with Madrid boss Zinedine Zidane describing him as the complete forward.
Kane was denied a potential winner in the second half by Keylor Navas, and Balague says his performance impressed Spanish media, but it was not their main focus after the game, with most of them turning their attention to Tottenham's tactics and their goalkeeper, Hugo Lloris.
"Perhaps there was too much talk about Harry Kane and Real Madrid, because this was about Spurs coming to the Bernabeu, and showing, like English teams have been showing at the moment, that they're at a new, higher level," Balague added.
"There is talk of Kane but you have to find it in page six or seven of the newspaper, it's not the biggest story.
"The specific tactics from Spurs for Real Madrid worked, and of course Hugo Lloris was outstanding. And that has all been reflected in the Spanish press."