Joe Montemurro's side have not conceded a goal throughout those successive victories, with their clean sheet still intact after Sunday's clash at Meadow Park.
Nobbs' first goal came after 27 minutes when she converted a Danielle Van De Donk cross.
Nobbs struck again to seal the victory after the interval, this time collecting a Vivianne Miedema pass which fell at the feet of the midfielder after some intervention from forward Beth Mead.
Tottenham extended their losing run to nine successive league games as they suffered a heavy 4-1 defeat at the hands of Manchester United.
Ella Toone opened the scoring for the hosts after just nine minutes, with Christen Press adding a second 10 minutes later.
Jess Sigsworth scored a third for Casey Stoney's Reds in the 31st minute, after which Toone struck again, stepping up to score a 48th-minute penalty awarded after Lucy Staniforth was brought down in the box.
United's clean sheet and four-goal advantage lasted until the third minute of stoppage time, when Spurs' Alanna Kennedy grabbed a consolation with a late free-kick.
Birmingham's winless league run was extended to 12 games as they had to settle for a 1-1 draw with Reading at Damson Park.
Ruby Mace put the home side ahead in the opening minutes, turning in a Sarah Mayling corner, but they eventually surrendered their lead when Reading's Rachel Rowe equalised in the 63rd minute.
Elsewhere, neither West Ham or Everton were able to find a goal as they played out a 0-0 draw at the Chigwell Construction Stadium.