It sounds like pip-tools[1] is what you want Pipenv to be.
1. Put your dependencies in requirements.in.
2. Run pip-compile to generate requirements.txt.
3. Commit both files.
4. Use requirements.txt in production.
You can also use setup.py or setup.cfg instead of requirements.in. This lets you build packages and specify dependencies like "Python 3.5+". requirements.in is simpler, though.