Russian Andreeva, who won the Adelaide International in January, has now won five WTA titles after breaking a clay-court title drought stretching back to 2024 ahead of next month's French Open.
"I was struggling a lot on how to find a solution to play against you today. You’re an amazing fighter and an even better person," Andreeva told Potapova during the presentation ceremony.
Andreeva made 14 unforced errors in the first set, twice as many as Potapova, who broke Andreeva twice to build a 4-1 lead and secured the set when the world number 10's forehand hit the net.
But Andreeva, a former French Open semi-finalist, became more aggressive in the second set, getting two breaks in a row to go 3-2 up before sealing it with an ace.
World number 97 Potapova, born in Russia and bidding to win the Linz Open for the second time, continued to make unforced errors and 18-year-old Andreeva served accurately to close out the win.
"Playing here for the first time as an Austrian, for me it means the world. All the support I was getting this week from the crowd, I never had it in my life. I am really thankful," said 25-year-old Potapova, who switched allegiance to Austria in December.