3V triggered switch using an IC
This is normally done by a level shifter but you don't need one. The 74HCT series is an HCMOS series compatible with TTL (hence the "T"). This means it will work with the TTL values for the minimum for a high input level, which is 2 V. So the 3 V output from the PIR is sufficiently high to be seen as a high level by the 74HCT86.

  

Odd, a 5 V device with a 3.3 V output, but it's also mentioned on Amazon...