
entscheidend
decisive
Determining the outcome of something; decisive for the result.
Sein Tor in der letzten Minute war entscheidend für den Sieg.
His goal in the last minute was decisive for the victory.
decisive / crucial
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decisive
Determining the outcome of something; decisive for the result.
Sein Tor in der letzten Minute war entscheidend für den Sieg.
His goal in the last minute was decisive for the victory.

crucial
Of very great importance or significance; essential.
Für den Erfolg des Projekts ist eine gute Kommunikation entscheidend.
Good communication is crucial for the success of the project.
'Entscheidend' is the present participle of the verb 'entscheiden' (to decide). So it describes something that is actively 'deciding' or determining a situation. This helps you understand the meaning 'ausschlaggebend' (decisive).
Der Schiedsrichter trifft die entscheidende Entscheidung.
The referee makes the decisive decision.
Very often, 'entscheidend' (decisive/crucial) is used with the preposition 'für' + accusative. This construction indicates what the importance or decisive influence relates to.
Die Unterstützung der Eltern war entscheidend für seinen Erfolg.
The support of his parents was decisive for his success.
'Entscheidend' (decisive/crucial) is often combined with nouns that describe a turning point or an important component. Typical examples are: 'der entscheidende Faktor' (the decisive factor), 'der entscheidende Moment' (the decisive moment), 'ein entscheidender Vorteil' (a decisive advantage), or 'die entscheidende Frage' (the crucial question).
Der entscheidende Faktor für den Sieg war die gute Teamarbeit.
The decisive factor for the victory was good teamwork.
A very common and formal expression is 'von entscheidender Bedeutung sein' (to be of crucial importance). It is used to emphasize the extraordinary importance of something.
Die pünktliche Lieferung der Teile ist von entscheidender Bedeutung für die Produktion.
The punctual delivery of the parts is of crucial importance for production.
important
Wichtig generally describes something that is highly significant for a goal. Entscheidend is stronger: a decisive factor determines the outcome or tips the scales. Both words can therefore fit, but entscheidend highlights the direct effect on the result.

Die richtige Antwort auf die letzte Aufgabe war für den Prüfungserfolg entscheidend.
The correct answer to the last question was decisive for success in the exam.
Eine gute Vorbereitung ist für den Prüfungserfolg wichtig.
Good preparation is important for success in the exam.