Mead took the lead at Bayliss Avenue on the half-hour mark when Richard Butler converted from the penalty spot.
Terry Spillane`s side then doubled their advantage seven minutes into the second period through Theo Fairweather-Johnson. Jack Carlile reduced the deficit for the Dockers 10 minutes later, but Mead held firm.
The gap between Thamesmead and fifth-placed Cray Wanderers is now seven points, a big a gap to close with only nine games remaining.
Ryman League
Follow us: @rymanleaguenews on Twitter | Ryman League group on Facebook
Keep up-to-date with our exclusive email newsletters.
Subscribe