World number five Pliskova be at Mihaela Buzarnescu 61 6-4 before Romanian Halep defeated Katerina Siniakova 6-4 6-0.
World number three Halep and pliskova meet in the reverse singles on Sunday.
Even the Czech Republic are seeking an 11th successive appearance within the last four.
Elsewhere two-time champions, in one top-tier ties France took a 2-0 lead after wins for world 19 Alize Cornet along with Caroline Garcia .
Garcia, coming back to the French squad for the first time since a people falling-out with her team mates at 20-16, be at Belgium number-two Alison van Uytvanck 7-6 (7-2) 4-6 6-2.
“There was a little stress, a small tension,” explained French number-one Garcia. “However, it had been exactly the same thing the last time I return to the team – nothing else, nothing more”
Cornet saw off Belgian world number 21 Elise Mertens 7-6 (8-6) 6-2 after an 82-minute starting series to pick up her first Fed Cup victory for five decades.
2017 runners-up Belarus was given that a 2-0 lead over Germany by straight-set victories for Aryna Sabalenka along with Aliaksandra Sasnovich.
The winners of this tie will face last year’s runners-up that the usa or winners Australia after the contest’s two successful nations ended the opening evening with a 1-1 draw.