As @TomdeGeus mentioned in the comments, this command works for me:
Python 3:
python3 -m pip install [package_name]
Python 2:
python -m pip install [package_name]
It’s best to not use the system-provided Python directly. Leave that one alone since the OS can change it in undesired ways, as you experienced.
The best practice is to configure your own Python version(s) and manage them on a per-project basis using virtualenv (for Python 2) or venv (for Python 3). This eliminates all dependency on the system-provided Python version, and also isolates each project from other projects on the machine.
Each project can have a different Python point version if needed, and gets its own site_packages directory so pip-installed libraries can also have different versions by project. This approach is a major problem-avoider.