The Spaniard backed up his maiden tour success at the Topshelf Open last month with a 6-3 4-6 6-2 triumph over Rosol that took one hour and 42 minutes to compile.
The win marks the latest chapter in the rise of the third seed, who is set to enter the top 20 of men's tennis for the first time when the updated rankings are released on Monday.
Bautista Agut had booked his spot in the final thanks to a straight-sets win over defending champion Fabio Fognini on Saturday.
Unseeded Czech Rosol was also relatively untroubled in his semi-final win, but his serve deserted him at key points of Sunday's decider at the ATP 250 event.
Bautista Agut made a superb start to the final, breaking at the first opportunity as he raced into a 3-0 lead.
And although he missed two set points in the eighth game, Bautista Agut's serve – from which he won 15 of 20 points on first serve – helped him take the opener in comfortable fashion.
In keeping with the tone of the first set, only one break was possible in the second, but it came in the decisive 10th game as Rosol broke to 15 to force a decider.
But Bautista Agut was always comfortable in the third and final set, with two early breaks helping him to a 4-0 lead.
And he never looked back as he became the ninth Spanish champion in Stuttgart and the sixth in the last 10 years.
Next year's MercedesCup will be played on grass, with this year's edition the final to take place on clay.