No. A pitcher cannot leave the game with his team losing and end the game winning. There is a hypothetical where a pitcher is losing a game, the game gets suspended due to rain, the player then gets traded to the other team, and he pitches the resumed game and ends up winning. However, rules of Baseball might prevent him playing in a game he'd started for the other team.
Yes. In the early days of baseball this was a common thing to have hapen. There was even a pitcher that pitched a double header and won both by shutout. His name was Ed Reulbach.
Not only has it been done in MLB, but (on occasion), a pitcher has WON both games -- and once the pitcher had a shutout IN BOTH GAMES.
Ernie Banks of the Chicago Cubs
Jim Bunning pitched a perfect game on June 21, 1964, at Shea Stadium in the first game of a double-header. Bunning threw 90 pitches with 10 strikeouts for a 6-0 win over the Mets.
"Double" means "Two", so there are two games in a double header.
Tim Lincecum for the San Fransisco Giants. Won games 1 and 5 in the 2010 world series.
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Jerry's Double Header - 1916 was released on: USA: 24 November 1916
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