Date-Krumm, 44, who was forced to qualify for the main draw, looked to be heading to a rapid defeat after Lisicki whizzed through the first set, winning 6-1.
But the ageless Japanese favorite fought back brilliantly to clinch a second set tie-break before wrapping up the decider to seal a 1-6, 7-6 (7/4), 6-2 triumph.
Date-Krumm will now play Ajla Tomljanovic in the second round. Tomljanovic defeated Vitalia Diatchenko 3-6, 6-0, 6-0 to advance.
Elsewhere Tuesday, both seeded players in action advanced safely, with eighth-seeded Ukrainian Elina Svitolina beating compatriot Kateryna Bondarenko, 4-6, 6-4, 7-5.
German fifth seed Angelique Kerber, meanwhile, had little difficulty in dispatching Russia`s Daria Gavrilova, winning 6-1, 6-3.
The field for this year`s Stanford tournament was weakened on the eve of the event when world number one Serena Williams withdrew with an injury as she builds towards her tilt at a calendar Grand Slam at the US Open.
With Williams out, Denmark`s Caroline Wozniacki is top seed.
Wozniacki, who received a bye in the first round, will play America`s Varvara Lepchenko in her first match.
Lepchenko outlasted Mirjana Lucic-Baroni, 3-6, 6-2, 7-6(4) to advance to the second round.