Saints were made to pay for their slow start as Jordan Nobbs' first-half brace proved the difference despite McGowan pulling one back with two minutes to go.
Former England international Nobbs scored within 15 seconds of kick-off to give visitors Newcastle the lead before adding a second midway through the first half.
This defeat has put a dent in Southampton FC's promotion hopes as they now sit sixth in the WSL 2, five points adrift of the play-off place.
Parker named an unchanged side after the win over Crystal Palace, while Newcastle's side included five former Saints players, Ashanti Akpan among them.
Newcastle took the lead straight from kick-off as Molly Pike won possession and released Nobbs, who rounded Fran Stenson and finished low into the far corner after just 15 seconds.
Saints responded well, with Ellie Brazil driving forward before finding Atlanta Primus, whose effort was gathered by Anna Tamminen.
Mary Bashford then dispossessed Aoife Mannion and fired goalwards, forcing Tamminen to concede a corner, before Stenson produced a strong save to deny Freya Gregory at the other end.
Bashford continued to threaten from the edge of the box but dragged a shot wide, before Nobbs struck again late in the first half, curling a fine finish into the top corner to double Newcastle’s lead.
After the restart, Michaela McAlonie tested Tamminen, while Bashford went close again with a first-time effort from a Jess Simpson cross.
Saints created chances throughout the second half but were unable to break down Newcastle’s defence, with Brazil hooking over late on.
Substitute McGowan pulled a goal back in the 88th minute, scoring her first Saints goal by poking home from a tight angle after a run down the right.
The late strike lifted Saints during six minutes of stoppage time, but the comeback fell short as the match ended in defeat.
Saints: Stenson, Simpson, Goddard, Bourne, Collett, Peplow, Bashford, Palmer, Brazil, Primus (Edwards, 86'), McAlonie (McGowan, 68').
Unused subs: Pettit, Brown, Mott, Hack, Watts, Roberts, Tucker, Archibald.
Newcastle: Tamminen, Wardlaw, Nobbs (Stokes, 86'), Purfield, Pike (Akpan, 77'), Gregory, Torpey, Sevenius (Lumsden, 58'), Joel, Mannion, Murphy.
Unused subs: Moan, Stokes, Hayles, Larsson.
Yellow cards: Purfield.
Attendance: 3,935.