All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Rinsing the mouth is putting water in the mouth and then spitting it out, or moving the water around inside the mouth and then spitting it out. Regardless of how the water is put in the mouth, if a person moves the water around inside his mouth with water and then spits it out, then he has rinsed his mouth.
Therefore, if you took water into your mouth directly from the faucet, and rinsed your mouth, then you will have performed ablution.
However, the Sunnah is to take water into your mouth and inhale it through your nose by three handfuls of water. So, you take a handful of water and rinse your mouth with some of it and rinse your nose with what remains of the water, and you do this three times. For more benefit, please refer to Fatwa 88886.
Allaah Knows best.