Patrick Wisdom homered as the Cubs ended a four-game losing streak.
They had been outscored 20-2 in dropping the first two games of the series at Milwaukee.
Stroman earned his first win for his new team in his fifth start.
Pitching on his 31st birthday, he struck out five and walked one.
Burnes struck out 10 in seven innings, giving up four hits. He retired the first 13 batters before Wisdom homered in the fifth.