A one-piece integral resilient grommet of elastomeric material is disclosed for isolating the vibration and noise which is propagated from a fractional horsepower motor. The resilient grommet has a central sleeve portion of resilient deformable material having a cylindrical axial opening. A pair of vibration dampening members are integrally formed on the center sleeve portion and have axially spaced apart end walls that extend radially from the central sleeve portion to define an annular recess for mounting the housing of the fractional horsepower motor. The grommet is attached to a support wall structure by a fastener that extends through the cylindrical axial opening and is brought into threaded engagement with the wall. To dampen the vibration wave propagation in the axial direction and isolate the noise of the motor from the support wall, the pair of vibration dampening members are each formed with a set of radially directed ribs which are angularly offset from each other.