Fake an injury and prepare for the interview during night time. As bad as it may sound, I faked a family emergency 15 mins prior to my interview and took-off. I did the whole charade - of picking up the phone, getting shocked and running out. I now work for the tier 1 firm I interviewed for. Work-life balance is pretty much shit but I can at least play around with the schedule a little.
I guess you have to be prepared like crazy and have your subject matter knowledge up to fleek to justify this risk (risk of annoying your current firm if you do this too much, you will only get so many shots at interviews, bird in hand vs two in the bus etc etc).
I asked for the interview to be scheduled between 7-9am. I explained the situation and the partner said (s)he was glad to be interviewing a morning person.
Either take a sick leave and give some excuse to your current employer regarding your health.
Or, tell your interviewer that there is some family emergency and you will be able to give interview at the specific timing only.
I now work for the tier 1 firm I interviewed for. Work-life balance is pretty much shit but I can at least play around with the schedule a little.