So common that Critical Success or Failure is literally mentioned in the 5e Dungeon Master's Guide (2014), though more as an enhancer rather than automatic success/failure.

The example's wording does imply that the roll result needs to be successful for the enhancer to apply. However, it literally states beforehand that it's up to the DM how it manifests, and increase of impact is just a suggestion.

Personally, I prefer what the example in the DMG implies than automatic success. It depends on the campaign, but giving a wizard with 8 strength a 1/20 chance to lift a Sequoia log by themself is a bit much.