But Williams fought hard, claiming the second set and rallying from 1-4 down in the final set to win the marathon match in just under three hours.
Four games and three match points later she found herself in the last 16 after nearly three hours on court.
The pair traded early breaks before Konta was handed the initiative and a second break when 21-year-old Mertens doubled-faulted four times in the same game to give Konta a 3-2 lead.
However, she remained more poised on the big points and eventually won on serve when Bertens could only tap the ball back across the net, allowing the 37-year-old American to put away the victor.
"I think I did a reasonably good job at sticking to the plan, and trusting that when it was going to bring me opportunities, I wanted to make sure that I was not giving her an opportunity to play", Konta said to the media after her win.
The match took almost three hours on the hottest day of the tournament so far and the 37-year-old would have to recover quickly to take on defending champion Johanna Konta.
The No. 11-seeded Konta advanced with much less drama, beating No. 22 Elise Mertens 6-2, 6-1.
"It didn't look good sometimes", Williams told the supportive crowd.More news: Man arrested after trying to disarm Rockford officer
More news: Ranking N. Korean official apparently visiting China
More news: John Mara talks Giants at league meeting
Del Potro won his first ATP Masters 1000 title last week in Indian Wells, California.
No. 2 Marin Cilic swept Vasek Pospisil 7-5, 7-6 (4).
Williams regrouped after a disastrous opening set, which she was four times a single point from winning.
The 29th seed had two match points on serve, which Williams saved before breaking in a tense finish. "And that's why I love this game".
"It was a very interesting match", Williams said afterwards.
"I felt everybody behind me", she told them. I had a lot of chances; she had a lot of chances. I hope I can get another win this year. This was my first big win.
Konta beat Williams in the semi-final on her way to the title a year ago, before toppling Wozniacki to lift the trophy - her last tournament victory.