Final answer:
Johannes Brahms was the significant late Romantic composer who balanced the emotional expression of Romanticism with a return to Viennese Classicism, holding onto Classical rules while also embracing Romantic harmony and melody.
Step-by-step explanation:
The important late Romantic composer who responded to the unbridled emotionalism of Romanticism with a return to a Viennese Classicism was Johannes Brahms. Brahms is considered a conservative composer who, while embracing the Romantic sensibilities of expression and emotion, continued to adhere to the structures and forms that characterized the Classical work of Haydn, Mozart, and Beethoven. Just as the Romantic era composers emulated the great classicists, Brahms's music is seen as a bridge between the periods, maintaining Classical rules in his compositions while employing the rich Romantic language of harmony and melody.
Romantic music often embodied intense human emotions and individual expression, vastly differing from the eighteenth-century focus on melodic and harmonic structures with clear forms. However, Brahms managed to blend the techniques, creating music that was both emotionally expressive and structurally sound. His approach was distinct within the period and positioned him as a key figure in the transition into the post-Romantic era, where nationalistic themes became more prevalent and composers like Mahler and Strauss pushed Romantic techniques to their limits.