The Williams sisters, long ago in careers that have spanned 20 years and 30 meetings as professionals, learned they had to view each other only as opponents - and in Serena's eyes, Venus is the best one she's ever played.
The 36-year-old Williams is looking for her 24th Slam singles title and seventh U.S. Open victory.
The match was easily Williams' most competitive in her first U.S. Open since her return to tennis after having her first child, and she let the crowd know it with a few screams after some key points.
Williams had lost only 11 games coming into the fourth round and looked set to cruise into the last eight after winning the first set in 18 minutes, but the unseeded Kanepi fought back.
Pliskova - a former world No. 1 and 2016 runner-up at Flushing Meadows - had earlier defeated Australia's Ash Barty in straight sets.
The 25-year-old American, who struggled mightily after her triumph last year, has since righted the ship and will be heavily favored to deny Sevastova from becoming the first Latvian woman to reach the semi-finals of the U.S. Open.
But Williams didn't back down from either challenge.
On Tuesday, Murray is likely to be named in the five-man squad for Great Britain's Davis Cup tie against Uzbekistan in Glasgow, beginning a week on Friday, and the last match played in the United Kingdom under the outgoing format of three days and best-of-five sets. "Not the best percentage, but I nearly made every point in the first serve game".
She played pitch-perfect tennis to outlast her elder sister after 71 minutes on Arthur Ashe Stadium.
'Obviously that level is definitely where she's going to want to stay during this whole tournament.
Meanwhile, defending men's champion Rafael Nadal beat Nikoloz Basilashvili Sunday 6-3 6-3 6-7 (6-8) 6-4 and will next face Dominic Thiem in the quarterfinals.
Recalling their clash, Williams said: "She came out strong".
And after getting to triple match point, she brought Kanepi to net and won with a passing shot. "A lot of things happen between", Pliskova said.
"Even though it's hard, especially for me", Serena said, "we just do the best that we can".