1 At the border
Your eVisa is tied electronically to the passport number you applied with. Officers read the passport and the record comes up. Paper adds nothing to that lookup — provided the passport number, full name exactly as printed in the machine-readable line, date of birth, nationality and passport expiry date on the approval match the passport you are holding.
2 At check-in, which is the real risk
Airlines are liable for carrying a passenger who is refused entry, so their staff often want to see the approval themselves before boarding. They are not obliged to accept "it is electronic". This is where travellers without a copy actually get stopped — before they ever reach Azerbaijan.
3 The practical answer
Carry both: a printed copy, and an offline copy on your phone. Do not rely on webmail, which needs signal and often a second authentication factor you cannot complete abroad.
4 The thing that actually invalidates it
Travelling on a different passport from the one you applied with. A renewed passport has a new number, so the electronic link does not resolve and the approval will not be found — printed or not. If you have renewed since applying, you need a new application, which takes 3 working days (sometimes around 5 hours where faster handling is possible — on request, never guaranteed).
5 Before you fly
Work through the Azerbaijan eVisa requirements checklist, then continue to the application flow. Other questions for this destination are collected in the Azerbaijan eVisa FAQ.
United eVisa Services is a private application-support provider, not a government agency. The immigration authority makes the decision.