Siegemund battled back to take her winning streak to six matches, four of which have come against top 10 players.
With all six scheduled matches on the main Manolo Santana court going the full three sets, the on-form Siegemund, fresh from winning in Stuttgart last week, and sixth seed Konta didn't get on court until just before midnight.
Konta appeared to have handled the long wait better as she took the first set 6-3.
However, Siegemund battled back to take her winning streak to six matches, four of which have come against top 10 players, by taking the final two sets 7-5, 6-4.
Eugenie Bouchard set up a potential mouth-watering second-round clash with Maria Sharapova by registering her first win on the WTA Tour since January's Australian Open over France's Alize Cornet 6-4, 4-6, 6-1.
Bouchard called Sharapova "a cheater" last week and suggested the Russian should be banned for life after testing positive for meldonium.
Sharapova faces Mirjana Lucic-Baroni in the first round on Sunday as the Russian continues her comeback from a 15-month ban.
"I hope I can play Maria," said Bouchard.
"Once I step on the court, everything will be to the side.
"But, you know, inside myself, I think I'll have a bit more motivation."
World number three Karolina Pliskova was the only seed in action on Saturday to survive and even the Czech was pushed hard by Lesia Tsurenko before winning 7-6 (7/5), 2-6, 6-2.
Ninth seed Madison Keys was beaten by Japan's Misaki Doi 6-4, 4-6, 6-4.
And 12th seed Elena Vesnina's poor form since winning in Indian Wells in March continued with a straight sets 6-4, 6-4 defeat to Romanian Irina Begu.