Are large language models (LLMs) creative in the same way humans are, and can the same interventions increase creativity in both? We evaluate a promising but largely untested intervention for creativity: forcing creators to draw an analogy from a random, remote source domain (''cross-domain mapping''). Human participants and LLMs generated novel features for ten daily products (e.g., backpack, TV) under two prompts: (i) cross-domain mapping, which required translating a property from a randomly assigned source (e.g., octopus, cactus, GPS), and (ii) user-need, which required proposing innovations targeting unmet user needs. We show that humans reliably benefit from randomly assigned cross-domain mappings, while LLMs, on average, generate more original ideas than humans and do not show a statistically significant effect of cross-domain mappings. However, in both systems, the impact of cross-domain mapping increases when the inspiration source becomes more semantically distant from the target. Our results highlight both the role of remote association in creative ideation and systematic differences in how humans and LLMs respond to the same intervention for creativity.