Every MLB Team's Longest Winning Streak Ever. 0 of 30. MLB superstars can carry their flawed teams for considerable stretches of the summer. Winning streaksâthe longest ones, at leastâare different phenomena. Many players must simultaneously overachieve. All 30 franchises have enjoyed temporary invincibility during a past regular season. Some for days, others for weeks, and yes, one club did for an entire month.