Companion cats often occupy the same anthropogenic niche as dogs in human families. Still, cat cognition remains an underrepresented research subject in ethology. Our goal was to examine whether two components that are crucial in dog-human communicative interactions (sensitivity to ostensive signals; gaze following) are also present in cats. In a two-object choice task, we used dynamic and momentary gazing in ostensive and non-ostensive communicative situations. We tested 41 cats at their owner's home. Cats on the group level achieved a 70% overall success rate, showing that they are capable of following human gaze as a referential cue. Cats' success rate was unaffected both by the type of gazing and the presence/absence of ostensive communication, showing that the subjects followed readily even the more difficult momentary cues. We found a trend (p = 0.085), showing that young cats (max. 1 year old) may achieve higher success rate than adult animals. Ostension had a significant effect on the latency of eye contact, which was the shortest when the experimenter called the cat's attention with ostensive signals (p = 0.006). Our results are the first that prove cats' ability to follow human gaze, which is considered to be one of the more difficult visual referential signals given during human-animal interactions. Although ostension did not affect the success rate of cats, we found ostensive human signals to be a more effective attention elicitor compared to non-ostensive vocalizations. Our study therefore provided the first insight to the existence of sensitivity to human ostension in another non-human species besides dogs. These results emphasize the possible relevance of the domestication process and responsiveness to socialization in the development of human-compatible socio-cognitive skills even in such animals as the cat, where the ancestor was not a highly social species.