Although she overpowered the German in a dominant second set, Stephens was made to work hard for the title, needing to first wrap up her rain-interrupted semi-final with former world number one Caroline Wozniacki 6-2 7-6(3) earlier on Saturday.
Their semi-final was suspended the previous evening with fifth seed Stephens leading 5-2 in the first set.
Stephens quickly sealed the opener upon resumption before prevailing in a second-set dog fight on a windswept centre court to set the platform for her triumph later in the day.
"You can never prepare for playing a set and then rain, then finishing the match the next morning and coming back again in the afternoon," Stephens told reporters.
"You just have to keep going and do your best."
The American, who stunned compatriot Serena Williams on her way to the Australian Open last four in 2013, was naturally delighted to claim an early-season title triumph ahead of the first grand slam of the season starting on Jan. 18.
"We have a really long season -- I have to play all the way until October -- so to win a tournament in the first week of the year is amazing," said Stephens, who later pulled out of next week's Hobart International with a viral illness.
"But I'm going to have many more opportunities throughout the year, and I'm looking forward to all of them. It's easier to look at it that way."
(Reporting by Ian Ransom in Melbourne and Sudipto Ganguly in Mumbai; Editing by John O'Brien)
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