It's hard finding the data for previous years, but the scenario you described actually happened in that same year, 2018, during the Azerbaijan Grand Prix.

According to the [FIA][1], these were the best sector times in qualifying:

- Sector 1: Kimi RAIKKONEN, 35.283
- Sector 2: Kimi RAIKKONEN, 40.704
- Sector 3: Esteban OCON 25.044

It gives us the combined "perfect lap": 1:41.031

However, the pole sitter was [Vettel][2], with 1:41.498, who, as you can see, had no fastest (purple) sector.

  [1]: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=2ahUKEwjI_vHiwefgAhVSXisKHeQmAQMQFjAAegQICBAC&url=https%3A%2F%2Fwww.fia.com%2Ffile%2F67715%2Fdownload&usg=AOvVaw1MAwyLxSbSEGb4kT4aOD6M
  [2]: https://en.wikipedia.org/wiki/2018_Azerbaijan_Grand_Prix