A sultry late afternoon on Key Biscayne was a different environment to their meeting at SW19, which saw Williams emerge an eventually comfortable victor for the loss of six games after Konta had spurned a few opportunities in the first set.
Bertens' confidence grew as Venus sent a forehand long to give her the chance to serve for the set at 6-5 and held to complete the seventh game in a row.
Konta, whose victory here previous year propelled her into the top 10 in the world rankings, advanced with relative ease, beating Belgian Elise Mertens 6-2, 6-1.
"It was a very interesting match", Williams said afterwards. She has bagged the title thrice - in 1998, 1999 and 2001. "It didn't look good sometimes but that's why you keep playing to the last point, and why I love this game".
The Eastbourne based player has risen impressively to the challenge, building on her first-round win over Kirsten Flipkens with an emphatic 6-2 6-1 win to see off the 22nd seed.
Konta has endured a poor 2018, but back-to-back straight-sets victories has lifted the Brit this week.
Like Konta, Ostapenko has also failed to hit the heights this year after a sensational French Open triumph in 2017. The British No. 1 took a ten-minute medical time-out after the second set, during which she had her lower back manipulated.
The Dutch, bidding for the fourth top 10 win after beating No.3 Kerber and No.9 Bacsinszky (2016 Roland Garros) and No.7 Vinci (2016 Nürnberg), got broken after a marathon game to 0-2 in the second set.
Williams faced more breakpoints in the third although this time the danger was averted, thanks to some powerful serves.
"In the tie-break, I showed my great tennis, and I won the match", Ostapenko said. "I just tried to hang in there, it was really not that much fun for that to happen, but that's tennis".
But US Open champion Stephens dominated Spain's reigning Wimbledon champion to record a 6-3 6-4 win and advance to the quarter-finals where she will face Germany's Angelique Kerber for a place in the semi-finals.
Puerto Rico's Puig followed up her upset of second-seeded Australian Open champion Caroline Wozniacki with a 6-3, 7-5 victory over Greece's Maria Sakkari.