Third seed Bautista Agut recovered from a slow start to win 2-6 7-6 (7-2) 6-4 in just under two hours at the ATP 250 event in s'Hertogenbosch.
The Spaniard was playing just his second ATP Tour final, having lost to Janko Tipsarevic in the showpiece at the Chennai Open last year.
But he held his nerve to complete an impressive comeback triumph on the grass just two days before Wimbledon begins.
Bautista Agut will face American Steve Johnson in the first round at the All England Club.
Becker – who opens Wimbledon against Donald Young – started superbly, claiming breaks in the third and fifth games of the first set.
That helped him into a 4-1 lead and serving confidently; he quickly wrapped up the opener.
Bautista Agut improved in the second set, winning 25 of 31 points on first serve, and neither player won a break point to force a tie-break.
Bautista Agut raced through that and then broke to take a 3-1 lead in the decider, a point from which the German never recovered, as his opponent celebrated a maiden ATP title.