The final was rained out on Sunday, with former two-time Munich champion Kohlschreiber leading 3-2 on serve.
Murray was in his first final on clay and won his 32nd career title, a welcome boost ahead of the French Open — the second Grand Slam of the season that is played on clay.
The top-ranked Williams broke Stephens four times and saved both break points she faced to secure her 25th straight win. Williams remained undefeated in 2015, with her last loss coming in round-robin play at last year's WTA finals.
Caroline Wozniacki powered past Christina McHale of the U.S., 7-5, 6-0.
Steve Johnson came from a set down to beat Alejandro Gonzalez of Colombia, 4-6, 6-3, 7-6 (4). The former USC star will next play third-seeded Rafael Nadal .