Victory also takes Murray's head-to-head record against Verdasco to 13-1.
The three-times grand slam victor, who cut a frustrated figure throughout an uncharacteristically sloppy performance, sealed victory with a powerful serve to claim his 45th career title. Where the balls are fairly heavy here on a quick court, he can generate a lot of power, he can control the ball.
"Winning is special regardless of your ranking", Murray said.
Murray will next meet French seventh seed Lucas Pouille who defeated Russian qualifier Evgeny Donskoy - the man who stunned Federer - 6-4, 5-7, 7-6 (7/2).
One particular shot to save the first match point of the tie breaker was described by Murray's former coach Mark Petchey as "the best of his career", while the breaker went on for so long that the players and umpires lost track of protocol and forgot to switch ends. "Neither of us served well at the beginning".
Despite the loss, Kohlschreiber was all smiles after the 2-hour, 55-minute quarterfinal.
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Having lost to Novak Djokovic in his first final of the year in Doha in January and then suffering a disappointing fourth-round exit at the Australian Open, victory allows Murray to head to America for the start of the Masters Series in fine form.
Despite a shaky serving performance, Murray, helped by a string of Verdasco errors, reeled off five successive games to take the first set 6-3.
Murray said told Sky Sports: "It's always nice to win any tournament but especially ones you haven't won before, so I'm very happy to do it here for the first time". "Then it was too late to come back".
Murray will face Spain's Fernando Verdasco, who beat Robin Haase of The Netherlands 7-6 (5), 5-7, 6-1 in Friday's first semifinal.
Women: Mirjana Lucic-Baroni bt Pauline Parmentier 6-2, 6-3; Lesia Tsurenko bt Jelena Ostapenko 6-3, 7-6 (5); Christina McHale bt Monica Puig 6-2, 6-2; Kristina Mladenovic bt Kirsten Flipkens 6-4, 6-3.
"He pushes you", Verdasco said.