The last qualifier to win a title on the main tour was Frenchman Nicolas Mahut at 's-Hertogenbosch in 2015.
The 95th-ranked Gojowczyk faced 12 aces from his French rival but put on a solid display on his own serve. He did not face a single break point and broke Paire three times to win the indoor tournament.
Gojowczyk is now set to rise to a career-high ranking of No. 66.
Paire, who had snapped an eight-match semifinal losing run on Saturday, was chasing a second title after claiming his maiden trophy in Bastad two years ago.
"He didn't miss many shots and it was tough for me," Paire said. "If I play like I did this week, I think I can do something good. There are a lot of positives."
French pair Julien Benneteau and Edouard Roger-Vasselin won the doubles title, beating Wesley Koolhof and Artem Sitak 7-5, 6-3.