
siegen
to win
To be the winner in a competition, battle, or conflict; to achieve a victory.
Nach einem spannenden Spiel siegte unsere Mannschaft mit 2:1.
After an exciting game, our team won 2–1.
to win
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to win
To be the winner in a competition, battle, or conflict; to achieve a victory.
Nach einem spannenden Spiel siegte unsere Mannschaft mit 2:1.
After an exciting game, our team won 2–1.

to prevail
In a figurative sense, to gain the upper hand or assert itself. Often refers to abstract concepts such as reason, justice, or love.
Am Ende siegte die Vernunft und sie fanden einen Kompromiss.
In the end, reason prevailed and they found a compromise.
'Siegen' (to win) is the verb in the word family around 'der Sieg' (the victory) and 'der Sieger' (the winner). If you know one of these words, you can understand the others more easily.
Nach dem Sieg feierte die ganze Mannschaft mit ihrem Siegerpokal.
After the victory, the whole team celebrated with their winner's trophy.
You can recognize the meaning from the subject of the sentence. If a person or a team is the subject, it is about a competition. If an abstract concept such as 'die Liebe' (love) is the subject, the figurative meaning is intended.
Am Ende siegte die Gerechtigkeit.
In the end, justice prevailed.
The verb 'siegen' (to win) is often used in an elevated or literary style, especially in the figurative meaning. It can sound more solemn or dramatic.
In den alten Legenden siegt der Held immer über das Böse.
In the old legends, the hero always triumphs over evil.
If you want to express whom someone won against, you use the preposition 'über' (over/against) with the accusative.
Die Heimmannschaft siegte klar über die Gäste.
The home team won clearly against the visitors.
In the figurative meaning, 'siegen' (to prevail) is often used with abstract, positive concepts as the subject. Typical examples are: reason, truth, good, or love.
Trotz aller Lügen hat am Ende die Wahrheit gesiegt.
Despite all the lies, truth prevailed in the end.
to win / gain
Gewinnen and siegen both refer to success in a competition. Gewinnen can take the competition or a prize as its object, while siegen highlights the winner and their triumph and usually appears without such an object. Use gewinnen with the competition and siegen when making a statement about the winner.

Unsere Mannschaft siegte im Finale am Samstag.
Our team triumphed in the final on Saturday.
Unsere Mannschaft gewann das Finale am Samstag.
Our team won the final on Saturday.