The unseeded Putintseva eliminated third seed Tatjana Maria of Germany 6-4, 6-7(6), 6-0. Putintseva converted six of 12 break points and saved nine of 11, overcoming Maria's 6-1 edge in aces.
Minnen, the seventh seed, ousted fourth seed Lucia Bronzetti of Italy 6-7(8), 6-4, 6-1.
Top seed Magda Linette of Poland avoided the upset in defeating fifth seed Rebeka Masarova of Spain 7-5, 7-6(6).
In the other quarter-final between unseeded players, China's Xiyu Wang needed three sets to get past Slovakian Viktoria Hruncakova 6-4, 4-6, 6-3.
Minnen faces Wang in one semi-final Friday, while Linette plays Putintseva.
Guadalajara Open Akron
American Caroline Dolehide overcame an early deficit to oust a confident Martina Trevisan of Italy 3-6, 7-6(9), 6-3 on Thursday in the quarter-finals in Guadalajara, Mexico.
Dolehide won 57 of 81 first-service points and saved eight of 12 break points to get past Trevisan, who eliminated top-seeded Tunisian Ons Jabeur on Wednesday. Dolehide also fended off a match point in the second-set tiebreaker before winning three straight points to force a third set that she ultimately prevailed in.
In the semi-finals, Dolehide will face countrywoman Sofia Kenin, who was a 6-4, 6-7(6), 6-1 winner over Canada's Leylah Fernandez on Thursday.
Greek number two seed Maria Sakkari beat Colombia's Emiliana Arango 6-3, 6-4 and third-seeded Caroline Garcia of France beat 10th-seeded Belarusian Victoria Azarenka by an identical score in the day's other quarter-final matches.
