試合 and 勝負: a match and deciding the outcome
Distinguish a sporting event from whether its contest has produced a winner.
The event itself
試合, read しあい, means match or game. 試合は午後に始まります。 says that the match starts in the afternoon.
試合を見に行きました。 means going to watch a match. It does not mean competing as a player.
Competing to win
勝負, read しょうぶ, refers to a contest or its outcome. 最後まで勝負が分かりませんでした。 says that the outcome was uncertain until the end.
勝負を決める一球でした。 describes a single ball or play with the ball that decided the contest. Context identifies the sport.
An ending and a result
試合は終わりましたが、引き分けでした。 says that the match ended in a draw. Ending a match does not necessarily establish a winner.
もう一度勝負しましょう。 proposes another contest. It does not report one already completed.
Does 試合は終わりました alone establish that there is a winner?
Show the answer and why
No. The ending and the win-or-loss outcome require separate attention.