World No.5 Pliskova gave the holder and No.1 seed the edge in Sunday's (AEDT) opening rubber as she swatted aside Mihaela Buzarnescu 6-1 6-4.
But reigning French Open champion Halep responded to get her country back on level terms in Ostrava, defeating Katerina Siniakova 6-4 6-0 to leave the tie poised at 1-1 ahead of her showdown with Pliskova.
"I expect a very tough one," Halep said. "It's Fed Cup, so the pressure is more but it's an open match and I think I'll fight for that chance and I'll be motivated, playing for my country."
Halep holds a 6-2 record in the head to head but Pliskova is unconcerned by that statistic.
"The match starts from zero-zero, so there's going to be a chance for both of us, never mind what happened in the past," she said. "I just have it in my head that I beat her [in the Fed Cup three years ago] when we won."
Meanwhile, in Liege, No.4 seed France is in control of its tie against Belgium, holding a 2-0 lead after Caroline Garcia defeated Alison Van Uytvanck 7-6 (7-2) 4-6 6-2 and Alize Cornet's 7-6 (8-6) 6-2 triumph over Elise Mertens, who will look to keep her nation's hopes alive against Garcia on Monday (AEDT).
Belarus is in a similarly strong position, thanks to Aliaksandra Sasnovich's 7-6 (7-3) 6-3 success over Tatjana Maria in Braunschweig combined with Aryna Sabalenka's 6-2 6-1 demolition of Andrea Petkovic. Sabalenka will seal Belarus' semi-final berth if she sees off Maria in the third rubber.
The last quarter-final tie to get under way was Australia's clash with No.2 seed United States, which pulled level at 1-1 in front of a noisy home crowd in Asheville.
Ashleigh Barty put Australia one up with a 6-1 7-6 (7-2) win over Sofia Kenin, but Madison Keys ensured it would be all-square heading into Monday (AEDT) thanks to a resounding 6-2 6-2 success over Kimberly Birrell.