The Polish world No 53 was forced to dig deep against Williams, who produced flashes of her power and athleticism in her first competitive match since the US Open in August.
But Linette’s consistency in the deciding set ultimately proved the difference.
Linette said she was pleased with the level she produced, even if she felt there was room for improvement.
"I thought I could have made fewer mistakes. Especially with such a powerful hitter, I need to be a bit more solid. So I’m glad that in the end, I managed to turn things around."
For Williams, 45, the loss was still an encouraging step as she continues her comeback after limited match play in recent seasons.
Despite fading in the third set, she showed she could still compete.
"I think my opponent, she played amazing. Definitely deserved the win," Williams said.
"She hung in there and I definitely felt like I had opportunities, which is great news for me, and I was able to put myself in a great position every game, almost to be able to convert."
Williams said the primary focus at this stage of her season was building match fitness and rhythm, particularly with the Australian Open looming.
"One of the biggest disadvantages for me is that everybody’s played more matches than I have," she said.
"So when the season starts like it does in tennis, and the first thing is a grand slam, then you got to come out hot, and I think I did come out hot.’’
New Zealander Monique Barry wished she could have done better in her 6-2, 6-1 loss to German Ella Seidel yesterday, but she did show her ability to fight to the end.
Ranked No726 in the world, compared to Seidel at No 84, this was always going to be a tough battle for the Kiwi No 2.
Although the more experienced player won, Barry, 23, never looked like waving the white flag.
"It was tough. I wish I could have done better," Barry said.
"I was trying to do what I could each point and hope to try and get in there and find some rhythm, but I just couldn't find that today, so I was a little bit disappointed, but happy that I kept trying every point and tried to find something to smile about out there."
In other matches, Italian Elisabetta Cocciaretto beat American Alycia Parks 6-2, 7-5, Briton Sonay Kartal downed Janice Tjen 6-1, 7-6 (7-4), 6-3, Croation Petra Marcinko defeated Colombian Camilia Osorio 6-4, 0-6, 7-6 (7-2) and Briton Katy Boulter beat Yuliia Starodubtseva 6-3, 6-3.
— Allied Media
