Stuart Nicholson marked his West Brom full debut with the opening goal as the Baggies strolled into the second round of the Carling Cup.
Greening's effort sealed a comfortable Baggies win
Nicholson scored his first senior goal with a rising shot from six yards following Richard Chaplow's shot which had been saved by Glyn Garner.
Orient enjoyed periods of pressure but were restricted to speculative efforts.
Darren Carter's spectacular strike made it safe for the Baggies and Jonathan Greening's low shot completed the rout.
Leyton Orient: Garner, Barnard, Lockwood, Fortune, Miller (McMahon 77), Tudor, Easton, Saah, Corden, Connor (Steele 72), Ibehre (Alexander 72).
Subs Not Used: Morris, Keith.
West Brom: Zuberbuhler, Wallwork, Curtis Davies, Robinson, McShane, Albrechtsen, Carter, Chaplow, Greening, Phillips (Hartson 76), Nicholson.
Subs Not Used: Steele, Quashie, Inamoto, Hodgkiss.
Booked: Nicholson, Carter, Robinson.
Goals: Nicholson 41, Carter 71, Greening 76.
Ref: K Wright (Cambridgeshire).